The Hamiltonian of a particle is $$H = \frac{{{p^2}}}{{2m}} + pq,$$ where q is generalised coordinate and p is the corresponding canonical momentum. The Lagrangian is
A. $$\frac{m}{2}{\left( {\frac{{dq}}{{dt}} + q} \right)^2}$$
B. $$\frac{m}{2}{\left( {\frac{{dq}}{{dt}} - q} \right)^2}$$
C. $$\frac{m}{2}\left[ {{{\left( {\frac{{dq}}{{dt}}} \right)}^2} + q\frac{{dq}}{{dt}} - {q^2}} \right]$$
D. $$\frac{m}{2}\left[ {{{\left( {\frac{{dq}}{{dt}}} \right)}^2} - q\frac{{dq}}{{dt}} + {q^2}} \right]$$
Answer: Option B
This Question Belongs to Engineering Physics >> Classical Mechanics
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