The general equations of analytical dynamics

Journal of Applied Mathematics and Mechanics

Volumn 60, Issue 6, 1996, Pages 899-909

  Rumyantsev, V V ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030520929     PISSN: 00218928     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8928(96)00112-8     Document Type: Article

References (33)

1. 1. POINCARÉ H., Sur une forme nouvelle des equations de la meanique. C. R. Acad. Sci Paris 132, 369-371, 1901.
2. 2. ČETAJEV N., Sur les équations de Poincaré. Dokl. Akad. Nauk SSSR 7, 103-104, 1928.
3. 3. CHETAYEV N. G., On Poincaré's equations. Prikl. Mat. Mekh. 5, 2, 253-262, 1941.
4. 4. CHETAYEV N. G., Poincaré's equations. In Theoretical Mechanics, Nauka, Moscow, 287-322, 1987.
5. 5. SHUROVA K. Ye., A variation of Poincaré's equations. Prikl. Mat. Mekh. 17, 1, 123-124, 1953; 18, 3, 384, 1954.
6. 5. SHUROVA K. Ye., A variation of Poincaré's equations. Prikl. Mat. Mekh. 17, 1, 123-124, 1953; 18, 3, 384, 1954.
7. 6. SHUROVA K. Ye., The principal invariant of equations in variations. Vestnik MGU. Ser. Mat. Mekh. Astron. Fiz. 3, 47-49, 1958.
8. 7. RUMYANTSEV V. V., The equations of motion of a rigid body with a cavity filled with liquid. Prikl. Mat. Mekh. 19, 1, 3-12, 1955.
9. 8. AMINOV M. Sh., The construction of groups of possible displacements. In Proceedings of the Interuniversity Conference on the Applied Theory of Motion Stability and Analytical Mechanics, 21-30. Kaz. Aviats. Inst., Kazan', 21-30, 1962.
10. 9. BOGOYAVLENSKII A. A., Cyclic displacements for the generalized area integral. Prikl. Mat. Mekh. 25, 4, 774-777, 1961.
11. 10. BOGOYAVLENSKII A. A., Theorems of the interaction between the parts of a mechanical system. Prikl. Mat. Mekh. 30, 1, 203-208, 1966.
12. 11. BOGOYAVLENSKII A. A., The properties of possible displacements for theorems of the interaction between the parts of a mechanical system. Prikl. Mat. Mekh. 31, 2, 377-384, 1967.
13. 12. FAM GUEN, On the equations of motion of non-holonomic mechanical systems in Poincaré-Chetayev variables. Prikl. Mat. Mekh. 31, 2, 253-259, 1967.
14. 13. FAM GUEN, On the equations of motion of non-holonomic mechanical systems in Poincaré-Chetayev variables. Prikl. Mat. Mekh. 32, 5, 804-814, 1968.
15. 14. FAM GUEN, One form of the equations of motion of mechanical systems. Prikl. Mat. Mekh. 33, 3, 397-402, 1969.
16. 15. MARKHASHOV L. M., On the Poincaré and Poincaré-Chetayev equations. Prikl. Mat. Mekh. 49, 1, 43-55, 1985.
17. 16. MARKHASHOV L. M., A generalization of the canonical form of Poincaré's equations. Prikl. Mat. Mekh. 51, 1, 157-160, 1987.
18. 17. MARKHASHOV L. M., On a remark of Poincaré. Prikl. Mat. Mekh. 51, 5, 724-734, 1987.
19. 18. MARKHASHOV L. M., Particular solutions of the equations of motion and their stability. Izv. Akad. Nauk SSSR. MTT 6, 26-32, 1987.
20. 19. RUMYANTSEV V. V., On the Poincaré-Chetayev equations. Prikl. Mat. Mekh. 58,3, 3-16, 1994.
21. 20. RUMYANTSEV V. V., On the Poincaré-Chetayev equations. Dokl. Ross. Akad. Nauk 338, 1, 51-53, 1994.
22. 21. LUR'YE A. I., Analytical Mechanics. Fizmatgiz, Moscow, 1961.
23. 22. DE LA VALLÉ-POUSSIN Ch.-J., Course d'Analyse Infinitésimale, Vol. 2. Gauthier-Villars, Paris, 1914.
24. 23. ARNOL'D V. M., Mathematical Methods of Classical Mechanics. Nauka, Moscow, 1989.
25. 24. MAGGIG. A., Da alcune nuove forma della equazioni della dinamica applicable ai sistemi anolonomi. Atti della Reale Accad. Naz. dei Lincei. Rend. Cl. fis. e. Math. Ser. 5. 10, 2, 298-291, 1901.
26. 25. WHITTAKER E. T., A Treatise on Analytical Dynamics of Particles and Rigid Bodies. Cambridge University Press, Cambridge, 1927.
27. 26. BOLTZMANN L., Uber die Form der Lagrange'schen Gleichungen for nicht holonome, generalisierte Koordinaten. Sitzungsb. der Wiener Akad. der Wissenschaften. Math.-Naturwiss. 140, 1-2, 1603-1614, 1902.
28. 27. HAMEL G., Die Lagrange-Eulerschen G leichungen der Mechanik. Z. Math. und Phys. 50, 1-57, 1904.
29. 28. RUMYANTSEV V. V., Parametric examination of dynamical nonholonomic systems and two problems of dynamics. Differential equations: Qualitative Theory 2nd Colloq. North-Holland, Amsterdam, 2, 833-919, 1987.
30. 29. JACOBI C. G. J., Vorlesungen über Dynamik. G. Reimer, Berlin, 1884.
31. 30. NEIMARK Yu. I. and FUFAYEV N. A., Dynamics of Non-holonomic Systems. Nauka, Moscow, 1967.
32. 31. VOLTERRA V., Sopra une classe di equazioni dinamiche. Atti della R. Accad. Delle Sci. di Torino 33, 451-475, 1897.
33. 32. KANE T. R., Dynamics of nonholomonic systems. Trans. ASME. Ser. E. J. Appl. Mech. 28, 4, 574-578, 1961.