1. General equation of motion of a machine
A machine is generally a one-degree-of-freedom system, i.e. the motion and mechanical actions involved can be expressed in terms of a single parameter, its first and second derivatives, and time.
We'll show that the equation of motion takes a unique form. Lagrange's method (see article of this treaty) is well suited to achieving this result.
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General form of kinetic energy
Since the system has a parameter q, for any point P, we formally have :
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General equation of motion of a machine
Solving the general equation
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