Nonholonomic systems revisited within the framework of analytical mechanics

Applied Mechanics Reviews

Volumn 51, Issue 7, 1998, Pages 415-433

  Ostrovskaya, S ^a   Angeles, J ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; MATHEMATICAL MODELS; MATRIX ALGEBRA;

LAGRANGE EQUATIONS; NONHOLONOMIC MECHANICAL SYSTEMS;

MECHANISMS;

EID: 0032123702     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.3099013     Document Type: Article

References (40)

1. Angeles J (1997), Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, Springer-Verlag, New York.
2. Angeles J and López-Cajún CS (1991), Optimization of Cam Mechanisms, Kluwer Academic Publ, Dordrecht.
3. Appell P (1899), Sur une forme nouvelle des équations de la dynamique, CRAcadSci, 459-460.
4. Appell P (1911), Exemple de mouvement d’un systéme assujetti à une liaison exprimée par une relation non linéaire entre les composantes de la vitesse, Rendic del Circolo Mat 32 48-50, Palermo.
5. Auslander L (1967), Differential Geometry, Harper, New York.
6. Brand L (1965), Advanced Calculus, John Wiley and Sons, New York.
7. Chaplygin S (1897), About a motion of a heavy body on a horizontal plan (O dvizhenii tyazhelogo tela vrashcheniya na gorizontalnoi ploskosti), In Izbrannye Trudy (A Collection), Klassiki Nauki, ch 3, 363—375, Nauka, Moscow (in Russian).
8. Choquet-Bruhat Y and DeWitt-Morette C (1989), Analysis, Manifolds and Physics - Part I: Basics, North-Holland, Amsterdam, New York.
9. Dobronravov VV (1970), Osnovy Mechaniki Negolonomnykh System (Fundamentals of the Mechanics of Nonholonomic Systems) (in Russian), Vyshaya Shcola, Moscow.
10. Euler L (1775), Formulae generales pro translatione quacunque corporum rigidorum, Novi Comm Acad Sci Petrop 20 189—207.
11. Frobenius FJ (1875), Über das Pfaffsche problem, J fiir die reine und angewandte Math 82 230—315.
12. Garcia de Jalón J and Bayo E (1994), Kinematic and Dynamic Simulation of Multibody Systems. The Real-Time Challenge, Springer-Verlag, New York.
13. Hamel G (1904), Die Lagrange-Eulerschen Gleichungen der Mechanik, Zeitschriftfur Math Phys 50, 1 -57
14. Hamel G (1938), Nichtholonome Systeme hõherer ART, Math Ges 37, 4152.
15. Hamel G (1949), Theoretische Mechanik, Springer-Verlag, Berlin.
16. Hamilton WR (1844), On quaternions: or a new system of imaginaries in algebra, Phi! Mag 25, 489-495.
17. Hartenberg RS and Denavit J (1964), Kinematic Synthesis of Linkages, McGraw-Hill, New York.
18. Hemami H and Weimer F (1981), Modelling of nonholonomic dynamic systems with applications, ASMEJ Appl Mech 48, 177-182.
19. Grigoryan AT and Pogrebysski IB (1972), History of Mechanics, Nauka, Moscow (Russian).
20. Huston RL and Passerello C (1974), On constraint equations: A new approach, ASME J Appl Mech 41, 1130-1131.
21. Isidori A (1989), Nonlinear Control Systems: An Introduction, Springer-Verlag, Berlin.
22. Kane TR (1961), Dynamics of nonholonomic systems, ASME J Appl Mech 28, 574-578.
23. Kane TR and Levinson DA (1985), Dynamics: Theory and Applications, McGraw-Hill, New York.
24. Lagrange JL (1788), Mécanique Analytique, Paris.
25. Lurie AI (1961), Analytical Mechanics (in Russian), Fizmatgiz, Moscow.
26. Maggi G (1896), Principii della Teoria Matematica del Movimento dei Corpi (Corso di Meccanica Razionale), Ulrico Hoepli.
27. Maggi G (1901), De alcune nuove forme delle equazioni della dinamica applicabli ai sistemi anolonomi, Atti Accad Naz Lincei Rend Cl Fis Mat Nat 10(5) 287-291.
28. Neimark J and Fufaev N (1972), Dynamics of Nonholonomic Systems, Translation of Mathematical Monographs, 33, Am Math Soc, Providence.
29. Newton I (1686), Philosophia Naturalis Principia Mathematica, London.
30. Papastavridis J (1994), On the Boltzmann-Hamel equations of motion: A vectorial treatment, ASME J Appl Mech 61, 453-459.
31. Passerello C and Huston RL (1973), Another look at nonholonomic systems, ASME J Appl Mech 40(1) 101-104.
32. Poinsot L (1851), Théorie nouvelle de la rotation des corps, Paris.
33. Reuleaux FR (1875), Theoretische Kinematic, Braunschweig.
34. Routh EJ (1905), Dynamics of a Systems of Rigid Bodies, Macmillan Co, London, New-York.
35. Saha S (1991), Dynamics and design of nonholonomic robotic mechanical systems, PhD Thesis, Dept of Mech Eng, McGill Univ, Montreal.
36. Seabra-Pereira MFO and Ambrósio JAC (ed) (1994), Computer-Aided Analysis of Rigid and Flexible Mechanical Systems, Kluwer Academic Publ, Dordrecht-Boston-London.
37. Szabó I (1977), Geschichte der Mechanischen Prinzipien und lhrer Wichtigsten Anwendungen, Birkhãuser Verlag, Basel.
38. Tzenoff I (1920), Sur les equations générales du mouvement des systémes matériels non holonomes, JMath 3,245-263.
39. Volterra V (1898), Sopra una classe di equazioni dinamiche, Atti R Acad sci 33, 451-476; Errata-corrige alia nota: Sopra una classe di equazioni dinamiche, (1900), 35, 118, Turin.
40. Voronetz P (1901), Ob uravneniyakh dvizheniya dlya negolonomnykh system (On equations of motion for nonholonomic systems), Matematicheskiy sbornik 22(4) (in Russian).