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<p>For a Lagrangian system with nonholonomic constraints, we discuss extensions of the equations of motion to sets of second-order ordinary differential equations. In the case of a purely kinetic Lagrangian, we investigate the conditions under which the nonholonomic trajectories are geodesics of a Riemannian metric, while preserving the constrained Lagrangian. We interpret the algebraic and PDE conditions of this problem as infinitesimal versions of the relation between the nonholonomic exponential map and the Riemannian metric. We discuss the special case of a Chaplygin system with symmetries, and we end the paper with some worked-out examples.</p>

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Geodesic Extensions of Mechanical Systems with Nonholonomic Constraints

  • 期刊论文

  • 发表日期：

    2025年2月12日

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  • Malika Belrhazi,
  • Tom Mestdag

摘要

For a Lagrangian system with nonholonomic constraints, we discuss extensions of the equations of motion to sets of second-order ordinary differential equations. In the case of a purely kinetic Lagrangian, we investigate the conditions under which the nonholonomic trajectories are geodesics of a Riemannian metric, while preserving the constrained Lagrangian. We interpret the algebraic and PDE conditions of this problem as infinitesimal versions of the relation between the nonholonomic exponential map and the Riemannian metric. We discuss the special case of a Chaplygin system with symmetries, and we end the paper with some worked-out examples.