Summary
In this paper we consider a dynamical system whose position is defined by a certain number of the Poincaré-Četaev variables and which moves with nonlinear nonholonomic constraints of Četaev's type. The canonical equations of motion of the system are derived and, for integrating them, a generalisation of the Hamilton-Jacobi theorem is presented.
Zusammenfassung
Für ein System mit nichtlinearen, nichtholonomen Bindungen vom Četaevschen Typ, dessen Lage sich durch eine gewisse Anzahl von Poincaré-Četaev-Variablen beschreiben lässt, werden kanonische Bewegungsgleichungen hergeleitet. Davon ausgehend wird eine Verallgemeinerung des Satzes von Hamilton-Jacobi aufgestellt.
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References
N.G.Četaev On Gauss's Principle, Iav. Fiziko-Mat. Obshch. Kazan. Univ. Ser. 3,6, 68–71 (1932–33).
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Q.K.Ghori,Hamilton-Jacobi Theorem for Nonlinear Nonholonomic Dynamical Systems, Z. angew. Math. Mech. Bd. 50–9, 563–564 (1970).
Q.K.Ghori andM.Hussain,Poincaré's Equations for Nonholonomic Dynamical Systems, Z. angew. Math. Mech. Bd. 53–7, 391–396 (1973).
K.E.Shurova,Some Properties of Poincaré Equations. Dissertation, Moscow State University (1958).
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Ghori, Q.K., Hussain, M. Generalisation of the Hamilton-Jacobi theorem. Journal of Applied Mathematics and Physics (ZAMP) 25, 536–540 (1974). https://doi.org/10.1007/BF01590678
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DOI: https://doi.org/10.1007/BF01590678