Lejeune Dirichlet theorem says that when potential energy has minima then equilibrium is stable, but that is sufficient condition. Can you give me example or examples where potential energy hasn't minima and equilibrium is stable. Tnx
I think we don't understand each other. My question is. If two lagrangians L'=L+\frac{df}{dt} and L gives us same dynamics. Why can't be that
\frac{\partial L}{\partial q}\delta q=\frac{df}{dt}?
I don't want more general symmetries than translation symmetries. I asked my question about invariance under translation symmetries. Can you answered the question about this problem which I asked?
If we watch some translation in space.
L(q_i+\delta q_i,\dot{q}_i,t)=L(q_i,\dot{q}_i,t)+\frac{\partial L}{\partial q_i}\delta q_i+...
and we say then
\frac{\partial L}{\partial q_i}=0
But we know that lagrangians L and L'=L+\frac{df}{dt} are equivalent. How we know that \frac{\partial...
Entropy is defined by:
S(A)=\int^{T_A}_0C_V\frac{dT}{T}
where A is state of the system in which temperature is T_A. When T_A\rightarrow 0 and C_V must go to zero. Why? And how fast does it go?
When people do Legendre transforms they suppose that U=U(S,V). But you can see in some books that heat is defined by:
dQ=(\frac{\partial U}{\partial P})_{V}dP+[(\frac{\partial U}{\partial V})_P+P]dV
So they supposed obviously that U=U(V,P).
In some books you can that internal energy is...