A GENERALIZATION OF THE CHETAEV CONDITION FOR NONLINEAR NONHOLONOMIC CONSTRAINTS: THE VELOCITY-DETERMINED VIRTUAL DISPLACEMENT APPROACH

作者：Li Shu Min^*; Berakdar Jamal

来源：Reports on Mathematical Physics, 2009, 63(2): 179-189.

DOI：10.1016/s0034-4877(09)00012-3

• nonlinear nonholonomic constraint
• velocity-determined virtual displacement
• relative velocity
• Chetaev model
• Appell-Hamel dynamical system

We present a formalism for nonlinear nonholonomic mechanical systems that generalizes the Chetaev model. Our treatment of the constrained problem is based on the velocity-determined virtual displacements. As an example, we discuss the Apell-Hamel dynamical system in the frame of a moving elevator and find the present method to provide results consistent with Newton's solution, in contrast to the other treatment generalizing the Chetaev condition based on a direct velocity expansion of the constraint equation. The known Chetaev condition follows as a special case of our scheme when the constraint is homogeneous in relative velocities.

• 出版日期2009-4