The factor which resist the motion of any dynamical system or The limitations and restrictions of motion of any dynamical system. Is called constraints !
Constraints can describe by the number of independent coordinate , needed to describe the motion of dynamical system ,
Generally constraint are two type :
➤ Holonomic constraint :
In simple way, if equation of constraint equality of equation of motion , Then constraint is Holonomic constraint.
For example , consider a particle moving of circumference of a circle ,
Constraints can describe by the number of independent coordinate , needed to describe the motion of dynamical system ,
Generally constraint are two type :
- Holonomic constraint
- Non-Holonomic constraint
➤ Holonomic constraint :
In simple way, if equation of constraint equality of equation of motion , Then constraint is Holonomic constraint.
For example , consider a particle moving of circumference of a circle ,
When particle moving on circumference of circle , two coordinate ( r , θ) , then only one coordinate sufficient to describe the motion of particle , because the radius of circle remain the same.
If ' r ' is position vector of the particles at any angular coordinate relative to the center of the circle, then
| r | = a , or , r-a = 0
This equation express constraint for the particle moving on the circumference of circle.
Similarly , we can study about , a particle moving on surface of sphere . There the correct coordinate ' r, θ , Φ , there θ , Φ only vary
So , degree of freedom is 2 .
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