Constraints | Classification and Properties of constraints | Classical mechanics

Constraints and its classification

Constraints force

• Constraints are restrictions that limit the motion of the particles of a system.
• Physically constrained motion is realized by the forces which arise when the object in motion is in contact with the constraining surfaces or curves. These forces are called constraint forces.

Properties of constraints force

They are elastic in nature and appear at the surface of contact.

They are so strong that they barely allow the body under consideration to deviate even slightly from a prescribed path or surface. This prescribed path or surface is called a constraint.

The effect of constraint force is to keep the constraint relations satisfied.




Classification of constraints

        Scleronomic and Rheonomic

• This classification is based on time.
• The constraints are said to be scleronomic constraints, if the constraint relations do not explicitly depend on time.
• But if the constraint relations explicitly depend on time then the constraints are said to be rheonomic.

        Holonomic and Non-holonomic

• This classification is based on velocity.
• If the constraint relations do not depend on velocities then such type of constraints are known as holonomic constraints.
• If the constraint relations depend on velocities then the constraints are said to be non-holonomic constraints.

        Conservative and Dissipative

• This classification is based on the work or total mechanical energy.
• If the constraint forces do not do any mechanical work or if the total mechanical energy of the system is conserved during the constraint motion then such type of constraints are known as conservative constraints.
• And if the constraint forces do mechanical work or the total mechanical energy of the system does not remain constant during the constraint motion then such type of constraints are known as dissipative constraints.

        Bilateral and Unilateral

• If the constraint relations are in the form of equation, not in the form of inequalities then the constraints are bilateral constraints.
• It means in bilateral constraints both forward and backward motion are possible at any point on the constraint surface.
• But if the constraint relations are in the form of inequalities, not in the form of equations then such type of constraints are known as unilateral constraints.
• In unilateral constraints, at any point of the constraints surface only forward or backward motion is possible.

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