Landau Lifshitz - Total time derivative of the Lagrangian

[omoplata]

On page 13 in Landau-Lifgarbagez Mechanics, the total time time derivative of the Lagrangian of a closed system is given to be,

$$\frac{d L}{d t} = \sum_i \frac{\partial L}{\partial q_i} \dot{q_i} + \sum_i \frac{\partial L}{\partial \dot{q_i}} \ddot{q_i}$$

Why does this stop here? I mean, why is the term $\sum_i \frac{\partial L}{\partial \ddot{q_i}} \dddot{q_i}$ not included?

An image of page 13 has been attached.

 

[Dickfore]

Because in classical mechanics the lagrangian is a function only of generalized coordinates and velocities. Read section 1 and 2 of the same book.

 

[omoplata]

Thanks for the reply Dickfore. You are correct.

 

[Dickfore]

It is a function of t only if the system is open.

 

[omoplata]

Thanks. Again you are correct.