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September 10, 2025Open Access

Hamilton-Jacobi Framework for Nonholonomic Dynamics

Key Points

The generalized Hamilton-Jacobi equations are derived for systems with nonholonomic constraints, enhancing understanding of their dynamics.
Evidence shows that equations from d’Alembert’s principle align with those derived from the variational action principle.
The proposed framework is illustrated through the analysis of a rolling disk on a plane and a knife edge on an inclined surface.
These findings may enable new approaches to solve complex dynamics in constrained mechanical systems.

Abstract

We derive generalized Hamilton–Jacobi equations for dynamical systems subject to nonholonomic constraints. The geometric formulation of Hamilton-Jacobi theory for nonholonomic constraints is developed, following the ideas of the authors in previous papers. It is shown that the equations of motion which follow from the principle of d’Alembert are identical to the equationswhich follow from the variational action principle. To illustrate the effectiveness of the proposed framework, we present and analyze two illustrative examples: the motion of a rolling disk on a horizontal plane and the motion of a knife edge on an inclined plane.

Hamilton-Jacobi Framework for Nonholonomic Dynamics

Key Points

Abstract

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