Question

A term of the type \( \frac{\partial T}{\partial q_k} \), where \( T \) and \( q_k \) are the kinetic energy and a generalized coordinate, respectively, if occurring in the equation of motion of a system is called a:

• A. Generalized momentum
• B. Generalized velocity
• C. Fictitious force
• D. Potential

Hint:

In Lagrangian mechanics, generalized momentum is obtained by differentiating the kinetic energy with respect to the generalized velocity.

Answer 1

The Correct Option is A

Generalized momentum is defined as:
\[ p_k = \frac{\partial T}{\partial \dot{q_k}} \] If \( \frac{\partial T}{\partial q_k} \) appears in the equation of motion, it refers to the generalized momentum.