Constrains and constrained motion

• A constrained motion is a motion which can not proceed arbitrary in any manner.
• Particle motion can be restricted to occur (1) along some specified path (2) on surface (plane or curved) arbitrarily oriented in space.
• Imposing constraints on a mechanical system is done to simplify the mathematical description of the system.
• Constraints expressed in the form of equation f(x₁,y₁,z₁,......,x_n,y_n,z_n :t)=0 are called holonomic constraints.
• Constraints not expressed in this fashion are called non-holonomic constraints.
• Scleronomic conatraints are independent of time.
• Constraints containing time explicitely are called rehonomic.
• Therefore a constraint is either

          "Scleronomic where constraints relations does not depend on time or rheonomic where constraints relations depends explicitly on time "
          and either
           "holonomic where constraints relations can be made independent of velocity or non-holonomic where these relations are irreducible functions of velocity"

Constraints types of some physicsl systems are given below in the table