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Constraints:
1. The limitation or restriction imposed on the motion of a particle or a system of particle
are known as constraints.
2. A constraint motion is a motion in which a particle can not proceed arbitrarily
in any manner ordirection.
3. The motion of particle is restricted to some specified paths only.
Examples:
•  In case of a simple pendulum, the motion is confined in a vertical plane. Two co-ordinates are required to describe the motion. The constraints is the fixed distance between point of suspension & bob of pendulum.
• For rigid bodies, the distance between any two particles is fixed is the constraint.
• A bead moving along a wire is fixed to move along the wire only that is one dimensional motion.
• A gas molecule is restricted by the walls of the container moving inside.
Types:
1.
a) Scleronomic: If constraint is explicitly time independent. Ex: Rigid Bodies
b) Rheonomic: If constraint is explicitly time dependent. Ex: Bead sliding on a moving                                  wire.
2.
a) Holonomic: If constraint relations are made independent of velocities. Ex: cylinder                                    rolling without sliding down an inclined plane.
b) Non-Holonomic: If constraint relations are dependent of velocities. Ex: A sphere                                                rolling without sliding down an inclined plane.
3.
a) Bilateral: If constraints are in the form of equations. Ex: Rigid bodies.
b) Unilateral: If constraint are expressed in the form of inequalities. Ex: Molecules in a                               gas container.
4.
a) Conservative: If force of constraint do not do any work. Ex: Simple Pendulum
b) Dissipative: If force of constraint do work. Ex: Pendulum with variable length.