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1. The limitation or restriction imposed on the motion of a particle or a system of particle
are known as constraints.
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.
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.
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.
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.
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.
b) Dissipative: If force of constraint do work. Ex: Pendulum with variable length.
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