# About lagrange dynamics of aparticle

## Main Question or Discussion Point

hi all ,

i am new at this forum , so i don't exactly know the rules about the topics and their sorting
i am self studying lagrange dynamics.
so my question is : when writing lagrange equations for aparticle ,& the particle
is in conformity with the constraints ; why the generalized forces
arenot containing the constraint forces ?

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Shooting Star
Homework Helper
Are you asking why the forces of constraint are not there in the equations explicitly?

Remember that for holonomic constraints, the number of independent generalized co-ordinates in the Lagrange's equation is less by the number of constraints from the actual number of co-ordinates. The equations contain the forces of constraint implicitly.

Last edited:
Are you asking why the forces of constraint are not there in the equations explicitly?

Remember that for holonomic constraints, the number of independent generalized co-ordinates in the Lagrange's equation is less by the number of constraints from the actual number of co-ordinates. The equations contain the forces of constraint implicitly.
how do i know that equations contain constraints explicity or implicity?

my question in other words :

why the constraint forces arenot included in the generalized forces resulted from applying lagrange equations on aparticle is in conformity with the constraints ?

Shooting Star
Homework Helper
my question in other words :

why the constraint forces arenot included in the generalized forces resulted from applying lagrange equations on aparticle is in conformity with the constraints ?
The whole technique of the Lagrangian treatment was developed so as to eliminate our calculating the forces of constraint.

Consider a simple example: a frictionless bead is moving on a frictionless wire in a plane in absence of gravity. The force of constraint would be the normal reaction of the wire directed radially inward, which would be equal to the centripetal force. That's how you would solve it to get the equations of motion, and show that it is moving with uniform linear and angular speed.

Now, why don't you do this very simple problem using Lagrange's equation yourself? You'll get a feel of what's happening.

Note that only one independent generalized co-ordinate theta is required. The fact that r is a constant, (or sqrt(x^2+y^2)) takes care of the normal reaction. The physical force of constraint, viz. the normal reaction, is equivalent to the equation r=constant.

The whole technique of the Lagrangian treatment was developed so as to eliminate our calculating the forces of constraint.

Consider a simple example: a frictionless bead is moving on a frictionless wire in a plane in absence of gravity. The force of constraint would be the normal reaction of the wire directed radially inward, which would be equal to the centripetal force. That's how you would solve it to get the equations of motion, and show that it is moving with uniform linear and angular speed.

Now, why don't you do this very simple problem using Lagrange's equation yourself? You'll get a feel of what's happening.

Note that only one independent generalized co-ordinate theta is required. The fact that r is a constant, (or sqrt(x^2+y^2)) takes care of the normal reaction. The physical force of constraint, viz. the normal reaction, is equivalent to the equation r=constant.
thanks , you are the man .