THEORETICAL MECHANICS
_______________________________________________________________________________________________________________________________________________________
PERSONAL RESEARCH
_______________________________________________________________________________________________________________________________________________________
Published articles
D. H. Delphenich, “On the general structure of mathematical models for physical systems,” Ann. Phys. (Berlin) 523 (2011), 965-989
D. H. Delphenich, “The homology of defective crystal lattices and the continuum limit,” Ann. Phys. (Berlin) 522 (2010), 874-903
D. H. Delphenich, “On the variational formulation of systems with non-holonomic constraints,” Ann. Phys. (Berlin) 18 (2009), 649-670.
D. H. Delphenich, “Integrability and the variational formulation of non-conservative mechanical systems,” Ann. Phys. (Berlin) 18 (2009), 45-56.
arXiv.org uploads
D. H. Delphenich, “Foliated Cobordism and Motion,” arXiv:gr-qc/0209091
D. H. Delphenich, “Groups of motions and mechanics I: point mechanics,” arXiv:0708.1572
D. H. Delphenich, “A generalization of Noether's theorem based on the virtual work functional,” arXiv:1109.0461
D. H. Delphenich, “On the topological nature of Volterra's theorem,” arXiv:1109.2012
D. H. Delphenich, "The representation of physical motions by various types of quaternions," arXiv:1205.4440.
D. H. Delphenich, "Mechanics of Cosserat media I: non-relativistic statics," arXiv:1212.0399
D. H. Delphenich, "The use of the teleparallelism connection in continuum mechanics," arXiv:1305.3477
D. H. Delphenich, "The role of homology in fluid vortices I: non-relativistic flow," arXiv:1412.3059
D. H. Delphenich, "Mechanics of Cosserat theory: II. relativistic theory, arXiv:1510.01243
_______________________________________________________________________________________________________________________________________________________
TRANSLATIONS
_______________________________________________________________________________________________________________________________________________________
Points and rigid bodies
A. F. Moebius, "On a special kind of dual relationship between figures in space," J. f. d. reine u. angew. Math. 10 (1833), 317-341.
G. Battaglini, "On the composition of forces," Rend. Accad. scienze fisiche Napoli 8 (1869), 23-32,
G. Battaglini, "On the theory of moments," Rend. Accad. scienze fisiche Napoli 8 (1869), 87-94,
G. Battaglini, "On dynames in involution," Rend. Accad. scienze fisiche Napoli 8 (1869), 166-167,
G. Battaglini, "On the infinitesimal geometric motion of a rigid system," Rend. Accad. scienze fisiche Napoli 9 (1870), 89-100,
F. Klein, “Note on the connection between line geometry and the mechanics of rigid bodies,” Math. Ann. 4 (1871); Ges. math. Abh., art. XIV, pp. 226-238.
L. Cremona, Reciprocal figures in graphical statics, Bernadoni, Milan, 1872.
A. Migiotti, "Reciprocal figures in graphical statics," Zeit. des osterr. Ingen. u. Arch.-Vereins (1873), 230-240.
A. Castigliano, "On the equilibrium of elastic systems," G. B. Paravia and Co., Turin, 1875.
H. Grassmann, "Mechanics, according to the principles of the theory of extensions," Math. Ann. 12 (1877), 222-240.
C. Geiser, "On a fundamental theorem in the kinematic geometry of space," J. f. d. reine u. angew. Math. 90 (1881), 39-43.
A. Voss, "On the differential equations of mechanics," Math. Ann. 25 (1885), 258-286.
G. Hauck, "On the reciprocal figures of graphical statics," J. f. d. reine u. angew. Math. 100(1887), 365-389.
S. Lie, “The infinitesimal contact transformations of mechanics,” Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaft zu Leipzig, Mathematische-Physische Classe, v. 41 (1889), 145-146.
C. Kuepper, "The screwing motion, the null system, and the linear complex," Monatsh. f. Math. u. Phys. (1890), 95-104.
E. Study, "On motions and transfers," Math. Ann. 39 (1891), 441-566.
F. Schur, "On the reciprocal figures of graphical statics," Zeit. Phys. 40 (1895), 48-53.
J. Luroth, "The motion of a rigid body," Zeit. f. Math. u. Phys. 43 (1898), 243-270.
H. Grassmann, Jr., "Screw theory and null systems," Inaugural lecture, Halle, 1899.
K. Zindler, Line geometry, with applications, v. I, Goschen, Leipzig, 1902.
A. Grunwald, "Sir Robert S. Ball's space of linear screws," Zeit. f. Math. u. Phys. 48 (1902), 49-108.
F. Klein, “On Sir Robert Ball’s theory of screws,” Zeit. Math. Phys. 47 (1902), republished with an appendix in Math. Ann. 62 (1906); Ges. math. Abh., art. XXIX, pp. 525-554.
E. Study, "General outline of a new method in kinematics," Appendix, Geometrie der Dynamen, B. G. Teubner, Leipzig, 1903.
E. Cotton, "Application of Cayley geometry in the geometric study of the displacement of a solid around a point," Ann. de l'E.N.S. (3) 20 (1903), 155-179.
F. Klein, “On stress surfaces and reciprocal diagrams, with special consideration of the Maxwell papers,” Archiv der Math. und Phys. 8 (8) (1904); Ges. math. Abh., Bd. 2, art. LXXVII.
E. Vessiot, “On the mechanical interpretation of infinitesimal contact transformations,” Bull. Soc. Math. de France 34 (1906), 230-269.
F. Klein, “On self-stresses of planar diagrams,” Math. Ann. 67 (1909), 433-444; Ges. math. Abh., Bd. 2, Springer, Berlin, 1973.
F. Pfeiffer, "On the statics of planar frameworks," Zeit. f. Math. u. Phys. 58 (1909-10), 262-272.
R. Weitzenbock, "On the system of forms of linear complexes in R3," Jber. d. Deut. Math.-Verein. 19 (1910), 225-238.
A. Schoenflies, "Simple derivation of the parameter formulas for motions and transfers," Rend. del Circ. mat. di Palermo (1) 9 (1910), 329-339.
W. Blaschke, “Euclidian kinematics and non-Euclidian geometry I, II,” Zeit. f. Math. und Phys. 60 (1911), 61-92; Ges. Werke, v. 2.
J. Gruenwald, "A mapping principle that links plane geometry and kinematics with spatial geometry," Sitz. d. Kaiserliche Akad. d. Wiss.: math-phys. Kl. 120, pt 2a (1911), 677-741.
K. Strubecker, "Kinematics, Lie's circle geometry, and the line-sphere transformation," Elemente der Mathematik 8 (1911), 4-13.
G. Hamel, “Statics of rigid bodies (theory),” excerpt from Elementare Mechanik: ein Lehrbuch, Teubner, Leipzig, 1912.
E. Study, "Foundations and goals of analytical kinematics," Sitzber. d. Berl. math. Ges. 13 (1913), 36-60.
H. Beck, "On linear manifolds of somas," Math. Ann. 81 (1920), 187-218.
H. Beck, "On improper somas," Math. Ann. 87 (1920), 152-156.
R. von Mises, “Motor algebra – a new tool for mechanics,” ZAMM 4 (1924), 155-181.
R. von Mises, “Applications of motor algebra,” ZAMM 4 (1924), 193-213.
E. A. Weiss, Introduction to line geometry and kinematics, Teubner, Leipzig, 1935.
L. de Broglie, "The relativistic variance of the kinetic moment of a rotating body," J. math. pures appl. 15 (1936), 89-95.
R. Sauer, Projective Line Geometry, De Gruyter, Berlin and Leipzig, 1937.
J. Lubanski, "New equations of motion for material systems in MINKOWSKI space," Acta Physica Polonica 6 (1937), 356-370.
O. Costa de Beauregard, "On the theory of proper kinetic moments in special relativity," J. math. pures appl. 21 (1942), 267-275.
A. Proca, "Point Mechanics," J. Phys. Rad. 15 (1954), 65-72.
A. Proca, "Particles with very large velocities in spinorial mechanics," Nuov. Cim. 2 (1955), 962-971.
W. Blaschke, “Applications of dual quaternions to kinematics,” Annales Academiae Scientiarum Fennicae, (1958), 1-13; Gesammelte Werke, v. 2.
W. Blaschke, "Kinematics and quaternions," VEB, Deutscher Verlag der Wissenschaften, Berlin, 1960.
Continuum mechanics
A. Clebsch, "On a general transformation of the hydrodynamical equations," J. f. d. reine und angew. Math. 54 (1857), 293-312.
G. Kirchhoff, "On the equilibrium and the motion of an infinitely-thin elastic rod," J. f. d. reine u. angew. Math. 56 (1858), 285-313.
A. Clebsch, "On the integration of the equations of hydrodynamics," J. f. reine u. angew. Math. 56 (1859), 1-10.
H. Helmholtz, "On discontinuous fluid motions," Monatsber. d. konigl. Akad. d. Wiss. zu Berlin (1868), 215-228.
M. Gebbia, "Fundamental propositions in the statics of elastic bodies," Rend. del Circ. mat. di Palermo (1) 5 (1891), 320-323.
W. Voigt, "Theoretical studies in the elastic behavior of crystals, I" Abh. d. Kon. Ges. d. Wiss. Gottingen (1892), 3-52.
H. Poincare, Theory of Vortices, Georges Carre, Paris, 1893.
E. Cesaro, "On the equilibrium of flexible, inextensible strings," from Lezioni di geometria intrinseca, from the author-publisher, Naples, 1896.
E. Cesaro, "On the equations of elasticity in hypersurface," from Lezioni di geometria intrinseca, from the author-publisher, Naples, 1896.
G. Kirchhoff, Lecture 26, (The dynamics of viscous fluids), from Vorlesungen uber mathematische Physik, v. I: Mechanik, Teubner, Leipzig, 1897.
G. Kirchhoff, Lecture 28, (Finite deformations of thin rods), from Vorlesungen uber mathematische Physik, v. I: Mechanik, Teubner, Leipzig, 1897.
G. Kirchhoff, Lecture 29, (InfInitesimal deformations of thin rods), from Vorlesungen uber mathematische Physik, v. I: Mechanik, Teubner, Leipzig, 1897.
G. Kirchhoff, Lecture 30, (Deformations of plates), from Vorlesungen uber mathematische Physik, v. I: Mechanik, Teubner, Leipzig, 1897.
I. Fredholm, "On the equations of equilibrium of a solid, elastic body," Acta Mathematica 23 (1898), 1-42.
W. Voigt, "The present state of our knowledge in the elasticity of crystals," Rapports presentes au congres international de physique, t. I, Gauthier-Villars, Paris, 1900; 277-362.
M. Jouguet," The vortex theorem in thermodynamics," J. math. pures et appl. 7 (1901), 235-257.
G. Weingarten, “On the surface of discontinuity in the theory of elasticity for solid bodies,” Rend. Reale Accad. dei Lincei, classe di sci., fis., mat., e nat., ser. 5 v. 10.1 (1901), 57-60.
M. Combebiac, "On the general equations of elasticity," Bull. Soc. math. Fr. 30 (1902), 108-110, 242-247.
M. Gebbia, "The typical deformations of elastic solid bodies," Ann. di. mat. (3) 10 (1904), 157-200.
E. Cesaro, "On VOLTERRA's formulas, which are fundamental in the theory of elastic distortions," Rend. Accad. delle sci. fis. Napoli 45 (1906), 311-321.
V. Volterra, "On the equilibrium of multiply-connected elastic bodies," Ann. Ec. Norm. Sup. (3) 24 (1907), 401-517.
E. Almansi, "On a particular class of deformations with polydromic displacements of cylindrical shells," Rend. Accad. dei Lincei (5) 16 (1907), 26-33.
G. A. Maggi, "On discontinuous, elastic displacements," Rend. Reale Accad. dei Lincei (5) 17 (1908), 571-576.
O. M. Corbino, "The tensions that are created in an elastic body by Volterra distortions and the consequent accidental double refraction," Rend. Reale Accad. dei Lincei (5) 18 (1909), 437-444.
E. Cosserat and F. Cosserat, Theory of deformable bodies, Hermann, Paris, 1909. (In two files: Chap. I-III, Chap. IV-VI)
E. and F. Cosserat, "Note on the theory of Euclidian action," excerpted from P. Appell, Traite de la mecanique rationelle, t. III, Gauthier-VIllars, Paris, 1910.
F. Klein, "On the formation of vortices in frictionless fluids," Zeit. Math. Phys. 58 (1910).
G. Herglotz, “On the mechanics of deformable bodies from the standpoint of relativity theory,” Ann. Phys. (Leipzig) (1911), 493-533.
J. Le Roux, " The angular deformations of continuous media," Travaux scientifiques de l'Universite de Rennes 10 (1911), 162-169.
J. Le Roux, "Research into the geometry of finite deformations," Ann. sci. de l'E.N.S. (3) 30 (1913), 193-245.
R. von Mises, "Mechanics of solid bodies in the plastically-deformable state," Nachr. d. Kgl. Ges. Wiss. Gottingen - Math.phys. Klasse 4 (1913), 583-592.
H. Weyl, "The asymptotic distribution law for the eigen-oscillations of an elastic body of arbitrary form," Rend. Circ. Mat. Palermo 34 (1914), 1-49.
C. Somigliana, “On the theory of elastic distortions,” Rend. Accad. Lincei 23 (1914), 463-472.
G. Armanni, “On the finite deformation of isotropic elastic solids,” Nuovo Cim., ser. 10 (1915), 427-447.
G. Colonetti, “On a reciprocity between deformation and distortions,” Rend. Accad. dei Lincei 24 (1915), 404-408.
C. Somigliana, "On the discontinuities in elastic potentials," Atti Reale Accad. scienze di Torino 51 (1915-16), 874-896.
E. Almansi, "The theory of distortions and the finite deformation of elastic solids," Rend. R. Acc. dei Lincei (5) 25 (1916), 191-192.
E. Almansi, "The ordinary theory of elasticity and the theory of finite deformations," Rend. R. Acc. dei Lincei (5) 26 (1917), 3-8.
G. A. Maggi, "Statement and solution of some questions related to the theory of elastic distortions," Rend. R. Acc. dei Lincei (5) 26 (1917), 350-357.
G. Colonetti, "On certain states of elastic co-action that do not depend upon external actions," Rend. Accad. dei Lincei (5) 26 (1917), 43-47.
H. Reissner, "Proper stresses and proper stress sources," Zeit f. Math. u. Mech. 11 (1931), 1-8.
P. Nemenyi, "A new method for singularities in the theory of elasticity," Zeit. f. angew. Math. und Mech. 11 (1931), 488-490.
P. Neményi, “Self-stresses in elastic structures,” Zeit. f. angew. Math. Phys. 11 (1931), 59-70.
A. Buhl, “Gravity, groups, and mechanics,” Chronicle des math. sci., v. LXII, Gauthier-Villars, Paris, 1934.
J. Sudria, "The Euclidian action of deformation and motion," Mem. des Sci. phys., fasc. 24, Gauthier-Villars, Paris,1935.
C. Weber, "Stress functions of the three-dimensional continuum," Zeit. angew. Math. Mech. 28 (1948), 193-197.
O. Costa de Beauregard, The Special Theory of Relativity, Masson and Co., Paris, 1949.
C. Moller, "On the dynamics of systems that have internal angular momentum," Ann. Inst. Henri Poincare 2 (1949), 251-278.
W. Gunther, "Stress functions and compatibility conditions in continuum mechanics," Anh. Braunschweig. Wiss. Ges. 6 (1954), 207-219.
E. Kroner, "The stress functions of three-dimensional, isotropic, elasticity theory," Zeit. Phys. 139 (1954), 175-188.
E. Kroner, "The stress functions of the three-dimensional, anisotropic, theory of elasticity," Zeit. Phys. 141 (1955), 286-398.
E. Kroner, "The fundamental connection between dislocation density and stress functions," Seit. Phys. 142 (1955), 463-475.
H. Schaeffer, "The stress functions of a dyname," Abh. Braunschweig. Wiss. Ges. 7 (1955), 107-112.
F. Halbwachs, G. Lochak, and J.-P. Vigier, "Decomposition of the energy-impulse of relativistic fluids endowed with an internal kinetic moment as a function of the dynamical variables," C. R. Acad. Sci. 241 (1955), 692-695.
F. Gallisot, “Exterior forms and the mechanics of continuous media,” Ann. Inst. Fourier 8 (1958), 291-335.
W. Günther, “On the statics and kinematics of Cosserat continua,” Abh. d. Braunsch. Wiss. Ges. 10 (1958), 195-213.
E. Kröner, “Continuum theory of dislocations and proper stresses,” Ergebnisse der angewandte Mathematik, Springer, Berlin, 1958.
E. Kröner, “General continuum theory of dislocations and proper stresses,” Arch. Rat. Mech. Anal. 4 (1960), 273-334.
G. Grioli, “Asymmetric elasticity,” Ann. Math. pura ed appl. 50 (1960), 389-417.
W. Gunther, "Analogous systems of shell equations," Ing.-Archiv 30 (1961), 160-186.
H. G. Schöpf, “General-relativistic principles of continuum mechanics,” Ann. Phys. (Leipzig) (7) 12 (1964), 372-395.
F. W. Hehl and E. Kroner, "Steps towards the material law for an elastic medium with moment-stresses," Z. Naturforschg. 20a (1965), 336-350.
S. Kessel, "On the compatibility conditions in a Cosserat continuum," Abh. Braunschw. Wiss. Ges. 17 (1965), 51-61.
H. Neuber, “On the problem of stress concentration in Cosserat bodies,” Acta Mech. II (1966), 48-69.
S. Kessel, “The stress functions of the Cosserat continuum,” Zeit. f. Angew. Math. Mech. 47 (1967), 329-336.
H. Schaefer, “Analysis of motor fields in Cosserat continua,” ZAMM 47 (1967), 319-328.
H. Schaefer, “The Cosserat continuum,” ZAMM 47 (1967), 485-498.
G. Kluge, “On the dynamics of the general theory of dislocations when moment stresses are considered,” Int. J. Eng. Sci. 7 (1969), 169-182.
G. Grioli, "Questions of compatibility for Cosserat continua," Symposia Mathematica, v. 1, Academic Press, London, 1969, pp. 271-287.
G. Ferrarese, "The thin shell, a simple example of a bi-dimensional continuous polar system," Symposia Mathematica, v. 1, Academic Press, London, 1969, pp. 327-355.
H. Schaefer, “A field theory of dislocations in a Cosserat continuum,” ZAMM 20 (1969), 891-899.
H. Schaefer, "The three-dimensional Cosserat continuum and the Cosserat shell in the calculus of differential forms," Symp. Math. I, Academic Press, London, 1969, pp. 253-269.
H. Schaefer, "The motor fields of the three-dimensional Cosserat continuum in the calculus of variations," Int. Centre for Mech. Sci., Courses and Lectures, no. 19, Udine, 1970.
S. Kessel, “Stress fields of a screw dislocation and an edge dislocation in a Cosserat continuum,” Zeit. f. Angew. Math. Mech. 50 (1970), 547-553.
G. Grioli, "Contribution to a formulation of integral type of the mechanics of Cosserat continua," Ann. Math. pura ed Appl. 111 (1976), 175-183.
E. Hölder, “G. Herglotz’s treatment of acceleration waves in his lectures on “Mechanik der Kontinua,” applied to the jump waves of Christoffel,” from E. B. Christoffel: the influence of his Work on Mathematics and the Physical Sciences,” ed. P. L. Butzer and F. Feher, Birkhäuser, Boston, 1981.
Non-holonomic systems
A. Voss, "On the differential equations of mechanics," Math. Ann. 25 (1885), 258-286.
G. Hamel, "On virtual displacements in mechanics," Math. Ann. 59 (1904), 416-434.
I. Tzenoff, "On the equations of motion of non-holonomic material systems," Math. Ann. 91 (1924), 161-168.
G. Hamel, “On non-holonomic systems,” Math. Ann. 92 (1924), 33-41.
G. Hamel, “Hamilton’s principle for non-holonomic systems,” Math. Ann. 111 (1935), 94-97.
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PERSONAL RESEARCH
_______________________________________________________________________________________________________________________________________________________
Published articles
D. H. Delphenich, “On the general structure of mathematical models for physical systems,” Ann. Phys. (Berlin) 523 (2011), 965-989
D. H. Delphenich, “The homology of defective crystal lattices and the continuum limit,” Ann. Phys. (Berlin) 522 (2010), 874-903
D. H. Delphenich, “On the variational formulation of systems with non-holonomic constraints,” Ann. Phys. (Berlin) 18 (2009), 649-670.
D. H. Delphenich, “Integrability and the variational formulation of non-conservative mechanical systems,” Ann. Phys. (Berlin) 18 (2009), 45-56.
arXiv.org uploads
D. H. Delphenich, “Foliated Cobordism and Motion,” arXiv:gr-qc/0209091
D. H. Delphenich, “Groups of motions and mechanics I: point mechanics,” arXiv:0708.1572
D. H. Delphenich, “A generalization of Noether's theorem based on the virtual work functional,” arXiv:1109.0461
D. H. Delphenich, “On the topological nature of Volterra's theorem,” arXiv:1109.2012
D. H. Delphenich, "The representation of physical motions by various types of quaternions," arXiv:1205.4440.
D. H. Delphenich, "Mechanics of Cosserat media I: non-relativistic statics," arXiv:1212.0399
D. H. Delphenich, "The use of the teleparallelism connection in continuum mechanics," arXiv:1305.3477
D. H. Delphenich, "The role of homology in fluid vortices I: non-relativistic flow," arXiv:1412.3059
D. H. Delphenich, "Mechanics of Cosserat theory: II. relativistic theory, arXiv:1510.01243
_______________________________________________________________________________________________________________________________________________________
TRANSLATIONS
_______________________________________________________________________________________________________________________________________________________
Points and rigid bodies
A. F. Moebius, "On a special kind of dual relationship between figures in space," J. f. d. reine u. angew. Math. 10 (1833), 317-341.
G. Battaglini, "On the composition of forces," Rend. Accad. scienze fisiche Napoli 8 (1869), 23-32,
G. Battaglini, "On the theory of moments," Rend. Accad. scienze fisiche Napoli 8 (1869), 87-94,
G. Battaglini, "On dynames in involution," Rend. Accad. scienze fisiche Napoli 8 (1869), 166-167,
G. Battaglini, "On the infinitesimal geometric motion of a rigid system," Rend. Accad. scienze fisiche Napoli 9 (1870), 89-100,
F. Klein, “Note on the connection between line geometry and the mechanics of rigid bodies,” Math. Ann. 4 (1871); Ges. math. Abh., art. XIV, pp. 226-238.
L. Cremona, Reciprocal figures in graphical statics, Bernadoni, Milan, 1872.
A. Migiotti, "Reciprocal figures in graphical statics," Zeit. des osterr. Ingen. u. Arch.-Vereins (1873), 230-240.
A. Castigliano, "On the equilibrium of elastic systems," G. B. Paravia and Co., Turin, 1875.
H. Grassmann, "Mechanics, according to the principles of the theory of extensions," Math. Ann. 12 (1877), 222-240.
C. Geiser, "On a fundamental theorem in the kinematic geometry of space," J. f. d. reine u. angew. Math. 90 (1881), 39-43.
A. Voss, "On the differential equations of mechanics," Math. Ann. 25 (1885), 258-286.
G. Hauck, "On the reciprocal figures of graphical statics," J. f. d. reine u. angew. Math. 100(1887), 365-389.
S. Lie, “The infinitesimal contact transformations of mechanics,” Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaft zu Leipzig, Mathematische-Physische Classe, v. 41 (1889), 145-146.
C. Kuepper, "The screwing motion, the null system, and the linear complex," Monatsh. f. Math. u. Phys. (1890), 95-104.
E. Study, "On motions and transfers," Math. Ann. 39 (1891), 441-566.
F. Schur, "On the reciprocal figures of graphical statics," Zeit. Phys. 40 (1895), 48-53.
J. Luroth, "The motion of a rigid body," Zeit. f. Math. u. Phys. 43 (1898), 243-270.
H. Grassmann, Jr., "Screw theory and null systems," Inaugural lecture, Halle, 1899.
K. Zindler, Line geometry, with applications, v. I, Goschen, Leipzig, 1902.
A. Grunwald, "Sir Robert S. Ball's space of linear screws," Zeit. f. Math. u. Phys. 48 (1902), 49-108.
F. Klein, “On Sir Robert Ball’s theory of screws,” Zeit. Math. Phys. 47 (1902), republished with an appendix in Math. Ann. 62 (1906); Ges. math. Abh., art. XXIX, pp. 525-554.
E. Study, "General outline of a new method in kinematics," Appendix, Geometrie der Dynamen, B. G. Teubner, Leipzig, 1903.
E. Cotton, "Application of Cayley geometry in the geometric study of the displacement of a solid around a point," Ann. de l'E.N.S. (3) 20 (1903), 155-179.
F. Klein, “On stress surfaces and reciprocal diagrams, with special consideration of the Maxwell papers,” Archiv der Math. und Phys. 8 (8) (1904); Ges. math. Abh., Bd. 2, art. LXXVII.
E. Vessiot, “On the mechanical interpretation of infinitesimal contact transformations,” Bull. Soc. Math. de France 34 (1906), 230-269.
F. Klein, “On self-stresses of planar diagrams,” Math. Ann. 67 (1909), 433-444; Ges. math. Abh., Bd. 2, Springer, Berlin, 1973.
F. Pfeiffer, "On the statics of planar frameworks," Zeit. f. Math. u. Phys. 58 (1909-10), 262-272.
R. Weitzenbock, "On the system of forms of linear complexes in R3," Jber. d. Deut. Math.-Verein. 19 (1910), 225-238.
A. Schoenflies, "Simple derivation of the parameter formulas for motions and transfers," Rend. del Circ. mat. di Palermo (1) 9 (1910), 329-339.
W. Blaschke, “Euclidian kinematics and non-Euclidian geometry I, II,” Zeit. f. Math. und Phys. 60 (1911), 61-92; Ges. Werke, v. 2.
J. Gruenwald, "A mapping principle that links plane geometry and kinematics with spatial geometry," Sitz. d. Kaiserliche Akad. d. Wiss.: math-phys. Kl. 120, pt 2a (1911), 677-741.
K. Strubecker, "Kinematics, Lie's circle geometry, and the line-sphere transformation," Elemente der Mathematik 8 (1911), 4-13.
G. Hamel, “Statics of rigid bodies (theory),” excerpt from Elementare Mechanik: ein Lehrbuch, Teubner, Leipzig, 1912.
E. Study, "Foundations and goals of analytical kinematics," Sitzber. d. Berl. math. Ges. 13 (1913), 36-60.
H. Beck, "On linear manifolds of somas," Math. Ann. 81 (1920), 187-218.
H. Beck, "On improper somas," Math. Ann. 87 (1920), 152-156.
R. von Mises, “Motor algebra – a new tool for mechanics,” ZAMM 4 (1924), 155-181.
R. von Mises, “Applications of motor algebra,” ZAMM 4 (1924), 193-213.
E. A. Weiss, Introduction to line geometry and kinematics, Teubner, Leipzig, 1935.
L. de Broglie, "The relativistic variance of the kinetic moment of a rotating body," J. math. pures appl. 15 (1936), 89-95.
R. Sauer, Projective Line Geometry, De Gruyter, Berlin and Leipzig, 1937.
J. Lubanski, "New equations of motion for material systems in MINKOWSKI space," Acta Physica Polonica 6 (1937), 356-370.
O. Costa de Beauregard, "On the theory of proper kinetic moments in special relativity," J. math. pures appl. 21 (1942), 267-275.
A. Proca, "Point Mechanics," J. Phys. Rad. 15 (1954), 65-72.
A. Proca, "Particles with very large velocities in spinorial mechanics," Nuov. Cim. 2 (1955), 962-971.
W. Blaschke, “Applications of dual quaternions to kinematics,” Annales Academiae Scientiarum Fennicae, (1958), 1-13; Gesammelte Werke, v. 2.
W. Blaschke, "Kinematics and quaternions," VEB, Deutscher Verlag der Wissenschaften, Berlin, 1960.
Continuum mechanics
A. Clebsch, "On a general transformation of the hydrodynamical equations," J. f. d. reine und angew. Math. 54 (1857), 293-312.
G. Kirchhoff, "On the equilibrium and the motion of an infinitely-thin elastic rod," J. f. d. reine u. angew. Math. 56 (1858), 285-313.
A. Clebsch, "On the integration of the equations of hydrodynamics," J. f. reine u. angew. Math. 56 (1859), 1-10.
H. Helmholtz, "On discontinuous fluid motions," Monatsber. d. konigl. Akad. d. Wiss. zu Berlin (1868), 215-228.
M. Gebbia, "Fundamental propositions in the statics of elastic bodies," Rend. del Circ. mat. di Palermo (1) 5 (1891), 320-323.
W. Voigt, "Theoretical studies in the elastic behavior of crystals, I" Abh. d. Kon. Ges. d. Wiss. Gottingen (1892), 3-52.
H. Poincare, Theory of Vortices, Georges Carre, Paris, 1893.
E. Cesaro, "On the equilibrium of flexible, inextensible strings," from Lezioni di geometria intrinseca, from the author-publisher, Naples, 1896.
E. Cesaro, "On the equations of elasticity in hypersurface," from Lezioni di geometria intrinseca, from the author-publisher, Naples, 1896.
G. Kirchhoff, Lecture 26, (The dynamics of viscous fluids), from Vorlesungen uber mathematische Physik, v. I: Mechanik, Teubner, Leipzig, 1897.
G. Kirchhoff, Lecture 28, (Finite deformations of thin rods), from Vorlesungen uber mathematische Physik, v. I: Mechanik, Teubner, Leipzig, 1897.
G. Kirchhoff, Lecture 29, (InfInitesimal deformations of thin rods), from Vorlesungen uber mathematische Physik, v. I: Mechanik, Teubner, Leipzig, 1897.
G. Kirchhoff, Lecture 30, (Deformations of plates), from Vorlesungen uber mathematische Physik, v. I: Mechanik, Teubner, Leipzig, 1897.
I. Fredholm, "On the equations of equilibrium of a solid, elastic body," Acta Mathematica 23 (1898), 1-42.
W. Voigt, "The present state of our knowledge in the elasticity of crystals," Rapports presentes au congres international de physique, t. I, Gauthier-Villars, Paris, 1900; 277-362.
M. Jouguet," The vortex theorem in thermodynamics," J. math. pures et appl. 7 (1901), 235-257.
G. Weingarten, “On the surface of discontinuity in the theory of elasticity for solid bodies,” Rend. Reale Accad. dei Lincei, classe di sci., fis., mat., e nat., ser. 5 v. 10.1 (1901), 57-60.
M. Combebiac, "On the general equations of elasticity," Bull. Soc. math. Fr. 30 (1902), 108-110, 242-247.
M. Gebbia, "The typical deformations of elastic solid bodies," Ann. di. mat. (3) 10 (1904), 157-200.
E. Cesaro, "On VOLTERRA's formulas, which are fundamental in the theory of elastic distortions," Rend. Accad. delle sci. fis. Napoli 45 (1906), 311-321.
V. Volterra, "On the equilibrium of multiply-connected elastic bodies," Ann. Ec. Norm. Sup. (3) 24 (1907), 401-517.
E. Almansi, "On a particular class of deformations with polydromic displacements of cylindrical shells," Rend. Accad. dei Lincei (5) 16 (1907), 26-33.
G. A. Maggi, "On discontinuous, elastic displacements," Rend. Reale Accad. dei Lincei (5) 17 (1908), 571-576.
O. M. Corbino, "The tensions that are created in an elastic body by Volterra distortions and the consequent accidental double refraction," Rend. Reale Accad. dei Lincei (5) 18 (1909), 437-444.
E. Cosserat and F. Cosserat, Theory of deformable bodies, Hermann, Paris, 1909. (In two files: Chap. I-III, Chap. IV-VI)
E. and F. Cosserat, "Note on the theory of Euclidian action," excerpted from P. Appell, Traite de la mecanique rationelle, t. III, Gauthier-VIllars, Paris, 1910.
F. Klein, "On the formation of vortices in frictionless fluids," Zeit. Math. Phys. 58 (1910).
G. Herglotz, “On the mechanics of deformable bodies from the standpoint of relativity theory,” Ann. Phys. (Leipzig) (1911), 493-533.
J. Le Roux, " The angular deformations of continuous media," Travaux scientifiques de l'Universite de Rennes 10 (1911), 162-169.
J. Le Roux, "Research into the geometry of finite deformations," Ann. sci. de l'E.N.S. (3) 30 (1913), 193-245.
R. von Mises, "Mechanics of solid bodies in the plastically-deformable state," Nachr. d. Kgl. Ges. Wiss. Gottingen - Math.phys. Klasse 4 (1913), 583-592.
H. Weyl, "The asymptotic distribution law for the eigen-oscillations of an elastic body of arbitrary form," Rend. Circ. Mat. Palermo 34 (1914), 1-49.
C. Somigliana, “On the theory of elastic distortions,” Rend. Accad. Lincei 23 (1914), 463-472.
G. Armanni, “On the finite deformation of isotropic elastic solids,” Nuovo Cim., ser. 10 (1915), 427-447.
G. Colonetti, “On a reciprocity between deformation and distortions,” Rend. Accad. dei Lincei 24 (1915), 404-408.
C. Somigliana, "On the discontinuities in elastic potentials," Atti Reale Accad. scienze di Torino 51 (1915-16), 874-896.
E. Almansi, "The theory of distortions and the finite deformation of elastic solids," Rend. R. Acc. dei Lincei (5) 25 (1916), 191-192.
E. Almansi, "The ordinary theory of elasticity and the theory of finite deformations," Rend. R. Acc. dei Lincei (5) 26 (1917), 3-8.
G. A. Maggi, "Statement and solution of some questions related to the theory of elastic distortions," Rend. R. Acc. dei Lincei (5) 26 (1917), 350-357.
G. Colonetti, "On certain states of elastic co-action that do not depend upon external actions," Rend. Accad. dei Lincei (5) 26 (1917), 43-47.
H. Reissner, "Proper stresses and proper stress sources," Zeit f. Math. u. Mech. 11 (1931), 1-8.
P. Nemenyi, "A new method for singularities in the theory of elasticity," Zeit. f. angew. Math. und Mech. 11 (1931), 488-490.
P. Neményi, “Self-stresses in elastic structures,” Zeit. f. angew. Math. Phys. 11 (1931), 59-70.
A. Buhl, “Gravity, groups, and mechanics,” Chronicle des math. sci., v. LXII, Gauthier-Villars, Paris, 1934.
J. Sudria, "The Euclidian action of deformation and motion," Mem. des Sci. phys., fasc. 24, Gauthier-Villars, Paris,1935.
C. Weber, "Stress functions of the three-dimensional continuum," Zeit. angew. Math. Mech. 28 (1948), 193-197.
O. Costa de Beauregard, The Special Theory of Relativity, Masson and Co., Paris, 1949.
C. Moller, "On the dynamics of systems that have internal angular momentum," Ann. Inst. Henri Poincare 2 (1949), 251-278.
W. Gunther, "Stress functions and compatibility conditions in continuum mechanics," Anh. Braunschweig. Wiss. Ges. 6 (1954), 207-219.
E. Kroner, "The stress functions of three-dimensional, isotropic, elasticity theory," Zeit. Phys. 139 (1954), 175-188.
E. Kroner, "The stress functions of the three-dimensional, anisotropic, theory of elasticity," Zeit. Phys. 141 (1955), 286-398.
E. Kroner, "The fundamental connection between dislocation density and stress functions," Seit. Phys. 142 (1955), 463-475.
H. Schaeffer, "The stress functions of a dyname," Abh. Braunschweig. Wiss. Ges. 7 (1955), 107-112.
F. Halbwachs, G. Lochak, and J.-P. Vigier, "Decomposition of the energy-impulse of relativistic fluids endowed with an internal kinetic moment as a function of the dynamical variables," C. R. Acad. Sci. 241 (1955), 692-695.
F. Gallisot, “Exterior forms and the mechanics of continuous media,” Ann. Inst. Fourier 8 (1958), 291-335.
W. Günther, “On the statics and kinematics of Cosserat continua,” Abh. d. Braunsch. Wiss. Ges. 10 (1958), 195-213.
E. Kröner, “Continuum theory of dislocations and proper stresses,” Ergebnisse der angewandte Mathematik, Springer, Berlin, 1958.
E. Kröner, “General continuum theory of dislocations and proper stresses,” Arch. Rat. Mech. Anal. 4 (1960), 273-334.
G. Grioli, “Asymmetric elasticity,” Ann. Math. pura ed appl. 50 (1960), 389-417.
W. Gunther, "Analogous systems of shell equations," Ing.-Archiv 30 (1961), 160-186.
H. G. Schöpf, “General-relativistic principles of continuum mechanics,” Ann. Phys. (Leipzig) (7) 12 (1964), 372-395.
F. W. Hehl and E. Kroner, "Steps towards the material law for an elastic medium with moment-stresses," Z. Naturforschg. 20a (1965), 336-350.
S. Kessel, "On the compatibility conditions in a Cosserat continuum," Abh. Braunschw. Wiss. Ges. 17 (1965), 51-61.
H. Neuber, “On the problem of stress concentration in Cosserat bodies,” Acta Mech. II (1966), 48-69.
S. Kessel, “The stress functions of the Cosserat continuum,” Zeit. f. Angew. Math. Mech. 47 (1967), 329-336.
H. Schaefer, “Analysis of motor fields in Cosserat continua,” ZAMM 47 (1967), 319-328.
H. Schaefer, “The Cosserat continuum,” ZAMM 47 (1967), 485-498.
G. Kluge, “On the dynamics of the general theory of dislocations when moment stresses are considered,” Int. J. Eng. Sci. 7 (1969), 169-182.
G. Grioli, "Questions of compatibility for Cosserat continua," Symposia Mathematica, v. 1, Academic Press, London, 1969, pp. 271-287.
G. Ferrarese, "The thin shell, a simple example of a bi-dimensional continuous polar system," Symposia Mathematica, v. 1, Academic Press, London, 1969, pp. 327-355.
H. Schaefer, “A field theory of dislocations in a Cosserat continuum,” ZAMM 20 (1969), 891-899.
H. Schaefer, "The three-dimensional Cosserat continuum and the Cosserat shell in the calculus of differential forms," Symp. Math. I, Academic Press, London, 1969, pp. 253-269.
H. Schaefer, "The motor fields of the three-dimensional Cosserat continuum in the calculus of variations," Int. Centre for Mech. Sci., Courses and Lectures, no. 19, Udine, 1970.
S. Kessel, “Stress fields of a screw dislocation and an edge dislocation in a Cosserat continuum,” Zeit. f. Angew. Math. Mech. 50 (1970), 547-553.
G. Grioli, "Contribution to a formulation of integral type of the mechanics of Cosserat continua," Ann. Math. pura ed Appl. 111 (1976), 175-183.
E. Hölder, “G. Herglotz’s treatment of acceleration waves in his lectures on “Mechanik der Kontinua,” applied to the jump waves of Christoffel,” from E. B. Christoffel: the influence of his Work on Mathematics and the Physical Sciences,” ed. P. L. Butzer and F. Feher, Birkhäuser, Boston, 1981.
Non-holonomic systems
A. Voss, "On the differential equations of mechanics," Math. Ann. 25 (1885), 258-286.
G. Hamel, "On virtual displacements in mechanics," Math. Ann. 59 (1904), 416-434.
I. Tzenoff, "On the equations of motion of non-holonomic material systems," Math. Ann. 91 (1924), 161-168.
G. Hamel, “On non-holonomic systems,” Math. Ann. 92 (1924), 33-41.
G. Hamel, “Hamilton’s principle for non-holonomic systems,” Math. Ann. 111 (1935), 94-97.
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