- #1
hideelo
- 91
- 15
I am trying to do go over the derivations for the principle of least action, and there seems to be an implicit assumption that I can't seem to justify. For the simple case of particles it is the following equality
δ(dq/dt) = d(δq)/dt
Where q is some coordinate, and δf is the first variation in f. In general, this can be seen more broadly, given a scalar field ψ
δ(∂ψ/∂x) = ∂(δψ)/∂x
Where x is any independant variable (i.e. x,y,z,t or any other coordinate system)
How are these equalities justified?
δ(dq/dt) = d(δq)/dt
Where q is some coordinate, and δf is the first variation in f. In general, this can be seen more broadly, given a scalar field ψ
δ(∂ψ/∂x) = ∂(δψ)/∂x
Where x is any independant variable (i.e. x,y,z,t or any other coordinate system)
How are these equalities justified?