Answer:

holonomic constraints are relations between the position variables (and possibly time[1]) that can be expressed in the following FORM:

{\displaystyle f(u_{1},u_{2},u_{3},\ldots ,u_{n},t)=0}{\displaystyle f(u_{1},u_{2},u_{3},\ldots ,u_{n},t)=0}

where {\displaystyle \{u_{1},u_{2},u_{3},\ldots ,u_{n}\}}{\displaystyle \{u_{1},u_{2},u_{3},\ldots ,u_{n}\}} are the n generalized coordinates that describe the system. For example, the motion of a particle constrained to lie on the surface of a sphere is subject to a holonomic constraint, but if the particle is able to fall off the sphere under the influence of gravity, the constraint becomes non-holonomic. For the first case the holonomic constraint may be given by the equation:

{\displaystyle r^{2}-a^{2}=0}{\displaystyle r^{2}-a^{2}=0}

where {\displaystyle r}r is the distance from the centre of a sphere of RADIUS {\displaystyle a}a, whereas the second non-holonomic case may be given by:

{\displaystyle r^{2}-a^{2}\geq 0}{\displaystyle r^{2}-a^{2}\geq 0}

Velocity-dependent constraints such as:

{\displaystyle f(u_{1},u_{2},\ldots ,u_{n},{\dot {u}}_{1},{\dot {u}}_{2},\ldots ,{\dot {u}}_{n},t)=0}{\displaystyle f(u_{1},u_{2},\ldots ,u_{n},{\dot {u}}_{1},{\dot {u}}_{2},\ldots ,{\dot {u}}_{n},t)=0}

are not usually holonomic seIn 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