# Time dependence of kinetic energy in Lagrangian formulation

• I
Ahmed1029
Could kinetic energy possibly depend explicitly on time in the lagrangian for some arbitrary set of generalized coordinates?

$$\vec{x}=\vec{x}(q^k,t), \quad k \in \{1,\ldots,f \}$$
$$\dot{\vec{x}}=\dot{q}^k \partial_k \vec{x} + \partial_t \vec{x}$$
$$T=\frac{m}{2} \dot{\vec{x}}^2 = \frac{m}{2} \left (\dot{q}^k \partial_k \vec{x} + \partial_t \vec{x} \right)^2,$$