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High order symmetric algorithms for nonlinear dynamical systems with non-holonomic constraints

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  • Man, Shumin
  • Gao, Qiang
  • Zhong, Wanxie

Abstract

Based on the Lagrange–d’Alembert principle and a modified Lagrange–d’Alembert principle, two kinds of symmetric algorithms with arbitrary high order are proposed for non-holonomic systems. The modified Lagrange–d’Alembert principle is constructed by adding an augment term to the Lagrange–d’Alembert principle, so that the non-holonomic constraints can be directly derived from variation. The high order algorithms are constructed by: (1) choosing control points to approximate generalized coordinates and Lagrange multipliers; (2) performing quadrature rules to approximate integrals; (3) choosing constraint points to satisfy non-holonomic constraints. The order of the presented algorithms is investigated numerically. The main factors to affect the accuracy of proposed algorithm were analyzed. Furthermore, the numerical algorithms are proven to be symmetric and can satisfy non-holonomic constraints with high precision.

Suggested Citation

  • Man, Shumin & Gao, Qiang & Zhong, Wanxie, 2023. "High order symmetric algorithms for nonlinear dynamical systems with non-holonomic constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 524-547.
    • Handle: RePEc:eee:matcom:v:212:y:2023:i:c:p:524-547
    DOI: 10.1016/j.matcom.2023.05.016
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    References listed on IDEAS

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    1. C. L. Hwang & L. T. Fan, 1967. "A Discrete Version of Pontryagin's Maximum Principle," Operations Research, INFORMS, vol. 15(1), pages 139-146, February.
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    1. Shumin Man & Qiang Gao & Wanxie Zhong, 2020. "Variational Integrators in Holonomic Mechanics," Mathematics, MDPI, vol. 8(8), pages 1-19, August.

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