# A question about Analytical Mechanics

1. Mar 19, 2007

### enricfemi

i am studing Analytical Mechanics in these days.it is really amazing. but a question pazzles me .it seems:

to generalized coordinates q,δq is arbitrary,it can equal 0;while variation in the x-coordinate, δx is not.

i just cann't understand

2. Mar 19, 2007

### Meir Achuz

In variation, delta x cannot be zero because you eventually divide by it.

3. Mar 20, 2007

### enricfemi

could you concretely explain why delta q can be zero.

thank you very much!

4. Mar 20, 2007

### enricfemi

i think when x is changed ,q should be also change.

help ,help ,can anybody help me?

5. Mar 21, 2007

### StatMechGuy

It depends on what your generalized coordinates are.

The derivation with variations like $$\delta q_i$$ depends on the variation possibly being anything at all. Lagrange's equations arise from the fact that you have a product of two functions in an integral that equals zero. Since the variation in the generalized coordinates could, in general, be anything, the other function has to be uniformly zero. Weinstock's book in Dover edition covers this point quite nicely.