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A constraint is a condition on the variables of a dynamical problem that the variables (or the physical solution for them) must satisfy. Normally, it amounts to restrictions of such variables to a lower-dimensional hypersurface embedded in the higher-dimensional full space of (unconstrained) variables.

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What are holonomic and non-holonomic constraints?

Suppose a particle is moving on the surface of the sphere, you can write the equation of the distance between the centre of the sphere and the particle( radius of the sphere) as $x^2+y^2+z^2 = R^2$, …
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