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I've just started studying mechanics. I need to find the properties of the constraint forces. I've gone through many books and also searched on internet but do not find any thing useful.

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  • $\begingroup$ What are the constraint forces you have in mind? $\endgroup$ – Steeven Aug 21 '17 at 19:53
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    $\begingroup$ Welcome to Physics Stack Exchange. This is a wonderful site for physics questions and answers. To get a good answer, we have to start with a good question. The question given here is so broad that no good answer can be given. Please ask something more specific. $\endgroup$ – DanielSank Aug 21 '17 at 22:13
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Constraint forces are those forces responsible for constraining the system to some geometric or kinematic conditions. For example, the force due to the string acting on the bob of a pendulum, the contact force done by a wire on a bead, the normal force the ground does on a block, the force by a light rod connecting two particles in a rigid dumbbell, etc. They are usually originated from interconnections (such as the light rod in the example above) but can also be related to external interactions (such as the contact force done by the wire or the normal force done by the ground).

In general, constraint forces are difficult to deal with in the realm of Newtonian Mechanics because they normally are not specified and depend implicitly on the form of the impressed or specified forces. For example, the tension acting on the bob of a pendulum enters Newton's second law as a variable depending on the bob's weight, the specified force. If we did not know the latter we would not know the former. Moreover, in some cases there are too many constraint forces which requires to many equations and makes it harder or even impracticable to solve the equations of motion.

One of the goals of analytical mechanics is to get rid of these constraint forces since they do not play any major role on the dynamics of the problem and keep only the specified forces. This can be done for a large class of systems, namely those which satisfy the Virtual Work Principle, i.e. the constraint forces are such that their total work on the system vanishes for any infinitesimal displacement respecting the constraints. The idea is that instead of writing down dynamical or equilibrium equations containing constraint forces we effectively replace them by kinematic equations and use them to eliminate some of the unknown variables. For example instead of writing two equations for the motion of the pendulum's bob in a fixed plane and taking into account both the tension along the string and the weight it is possible to neglect the constraint force by assuming that the bob moves along a fixed circle.

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