Dot cancellation (holonomic constraints)

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SUMMARY

The discussion focuses on the concept of dot cancellation in holonomic constraints as defined in Analytical Mechanics. It establishes that for holonomic constraints represented by the equation r = r(q1, q2, ... qn, t), the relationship ∂r'/∂q_k' = ∂r/∂q_k holds true. Two examples are analyzed: a mass sliding down a frictionless inclined plane and a rotating bead on a wire, emphasizing the need to express the position r in terms of generalized coordinates.

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  • Understanding of holonomic constraints in classical mechanics
  • Familiarity with generalized coordinates
  • Basic knowledge of derivatives in multivariable calculus
  • Concept of analytical mechanics and its principles
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Students of physics, mechanical engineers, and anyone studying classical mechanics, particularly those interested in holonomic constraints and their applications in analytical mechanics.

amiras
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I started to read Analytical Mechanics. It said that if holonomic constraints are defined as:

r = r(q1, q2, ... qn, t) (or without time)

This equation holds (dot cancellation):

∂r'/∂q_k' = ∂r/∂q_k

where ' specified derivatives.

And the question was given to check if it works for two simple examples:

1) a mass sliding without friction down a stationary inclined plane
2) the rotating bead on a wire

So if we talk about 1) I should express the position r with some generalized coordinate?
 
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The position r is the generalised coordinate
 

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