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In this chapter, we state the governing principles for deriving the equations of motion for a system with nonholonomic constraints linear in velocities. We start with the discussion of the validity of such constraints and state Lagrange-D’Alembert’s principle, allowing us to compute the equations of motion. We apply this principle to several examples, such as a coin rolling vertically on a horizontal plane, a skate on an inclined plane, and Chaplygin’s sleigh.

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Nonholonomic Constraints

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  • 发表日期：

    2025年

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  • Vakhtang Putkaradze

摘要

In this chapter, we state the governing principles for deriving the equations of motion for a system with nonholonomic constraints linear in velocities. We start with the discussion of the validity of such constraints and state Lagrange-D’Alembert’s principle, allowing us to compute the equations of motion. We apply this principle to several examples, such as a coin rolling vertically on a horizontal plane, a skate on an inclined plane, and Chaplygin’s sleigh.