# constraints in physics (classical mechanics) with examples

In this article learn about Constraints in physics used in classical mechanics. Constraints limit the motion of the system. We can use constraints to find the degrees of freedom that that must be calculated before solving dynamical problems.

## Constraints

• A constrained motion is a motion which cannot proceed arbitrarily in any manner.
• Particle motion can be restricted to occur (1) along with some specified path (2) on the 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 $f(x_1,y_1,z_1,……,x_n,y_n,z_n :t)=0$ are called  holonomic constraints.
• Constraints not expressed in this fashion are called non-holonomic constraints.
• Scleronomic constraints are independent of time.
• Constraints containing time explicitly 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

or

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 physical systems are given below in the table