constraints and types of constraints

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Restriction or limitation to the motion of particles due to forces is called constraint. 

Types of constraints 

1. Holonomic Constraints:

If all constraints of the system can be expressed as equations having the form f(q1,q2,....., qs) = 0 or their equivalent, then the system is said to be holonomic and the constraints are holonomic constraints. 

Example:

* If there’s a sphere or circle of radius a, such that a particle is bound to move on its boundary 

We have 

r=a

Or r-a= 0

In other words, 

f(q1,q2,.....,qs) = 0

Such a constraint is called holonomic constraint. 

* A cylinder rolling without slipping down a rough surface inclined at an angle a.

* A horizontal cylinder of radius a rolling inside a perfectly rough hollow horizontal cylinder of radius b>a. 

2. Non-holonomic constraint

If the particle cannot move in the boundary or cannot move up to radius distance, we can say

r does not equal 0

Or r-a is not equal to 0.

Also, we can write r<a.

Such constraints are called non-holonomic. Here,

 f(q1,q2,.....,qs) does not equal 0 

For example,

A sphere constrained to roll on a perfectly rough plane.

A sphere rolling down from the top of a fixed sphere.

Scheleronomic Constraint: 

This constraint is independent of time. For example, if a simple pendulum has an inextensible length. In other words, its length does not change as time changes. 

Rheonomic Constraint: 

This constraint is dependent on time. For example, if the length of the pendulum changes with time, the constraints are Rheonomic.