- #1
eljose
- 484
- 0
Let be an statistical system of N particles with their Hamiltonian..
H=\sum_{i=0}^{N}\frac{p_{i}^{2}}{2m}+V(q1,q2,...,qN)
then you could obtain their equations of motion in the form:
dp_{i}/dt=-dH/dp_{i} and dq_{i}/dt=p_{i}/m
but of course if N is big you could take years and years to solve it..but there wouldn,t be an easier formula..(or an approach) to obtain and solve Newton,s equation of motion for this system (considering stochastic or similar) by means of a functional of the q,s in the sense Q(q1,q2,q3,q4,...qN)
H=\sum_{i=0}^{N}\frac{p_{i}^{2}}{2m}+V(q1,q2,...,qN)
then you could obtain their equations of motion in the form:
dp_{i}/dt=-dH/dp_{i} and dq_{i}/dt=p_{i}/m
but of course if N is big you could take years and years to solve it..but there wouldn,t be an easier formula..(or an approach) to obtain and solve Newton,s equation of motion for this system (considering stochastic or similar) by means of a functional of the q,s in the sense Q(q1,q2,q3,q4,...qN)
