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The Birkhoffian expression of a Boltzmann-Hamel equation of nonholonomic system and its generalized symplectic geometric algorithm. (Chinese. English summary) Zbl 1289.70019
Summary: For a Boltzmann-Hamel equation of nonholonomic mechanical system, when it meets certain conditions, the Boltzmann-Hamel equation can be transformed into a Birkhoffian system. By constructing the generating function, the system is investigated numerically using the generalized symplectic geometric algorithm of the nonautonomous Birkhoffian system. Compared with the above-mentioned algorithm with the classical Runge-Kutta method, Birkhoffian symplectic scheme is very accurate in a long-term tracing.

MSC:
70F25 Nonholonomic systems related to the dynamics of a system of particles
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
70H45 Constrained dynamics, Dirac’s theory of constraints
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