Answer to Question #212168 in Mechanics | Relativity for Anita

Question

The Hamiltonian of a system is given in the form of the equation H = 1/2 (1/q^2 + p^2 q^4)

Write down the equation of motion for q !

Answer 1

We know that

$-\dot{p}=\frac{dH}{dq},\dot{q}=\frac{dH}{dp}$

$-\dot{p}=\frac{d}{dq}(\frac{1}{2q^2}+\frac{p^2q^4}{2})$

$\dot{p}=\frac{1}{q^3}-p^2q^3$

$\dot{q}=\frac{dH}{dp}$

$\dot{q}=\frac{d}{dp}(\frac{1}{2q^2}+\frac{p^2q^4}{2})$

$\dot{q}=pq^4\rightarrow{1}$

Equation (1) is called eqution of motion q