DOI: 10.5176/2251-1911_CMCGS16.17
Authors: John W. Perram
Abstract: Without appealing to the principle of virtual work, we derive a criterion for the validity of D'Alembert's equations of motion for mechanical systems subject to time-dependent holonomic constraints. This criterion is derived on the basis of a condition that the forces of constraint do no work in real motions. We show that this criterion is satisfied by mechanical systems composed of rigid bodies connected by universal, revolute (rotational) and telescopic joints, when
the motion of one or more of the rigid bodies is prescribed externally. We then present a derivation of D'Alembert's equations of motion using only vector calculus and linear algebra. Our conclusion is that the principle of virtual work, a source of puzzlement to generations of students and teachers of mechanics, can be finally put to rest.
Keywords: Time-dependent constraints, D'Alembertian equations of motion, Principle of virtual work, Universal joints, Revolute joints, telescopic joints
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