A Simple Method for Solving Dynamic Problems of Robotics

Abstract:

In this paper we find a general solution for the action function in the case of a heavy point moving on a sphere using the method of separation of the Hamilton-Jacobi equation variables. The solution contains two constants: the energy of a material point and the momentum projection onto a horizontal direction. We analyze the modes of a spherical pendulum oscillation. It is shown that the solution does not contain any errors of accumulation which are characteristic for evolution problems with long prediction periods.

• Periodical: Applied Mechanics and Materials (Volume 756)
• Pages: 552-555
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.756.552
• Online since: April 2015
• Authors: Aleksey M. Bubenchikov, Eduard E. Libin, Yulia P. Hudobina
• Keywords: Jacobi Method, Many-Valued Integrals, Spherical Pendulum

References

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