Lagrange's method under external force

[hatepod]

Let us suppose that I have an isolated box which contains some masses connected with springs etc.

When this box is stationary in the inertial frame, I can use lagrange's method to solve all coordinates related with the masses and springs without any problem.

However, let us also suppose that I started to move this box such that one fixed point on the box has a known acceleration (a) and a known rotation rate (w).

Under this condition, is there anyway to use Lagrange's formulation to compute the coordinates of masses and springs inside the box as a function of (a) and (w)?

 

[Valerie Park]

The answer is yes. In this case, the coordinates of the masses and springs can be computed using the equations of motion in a non-inertial frame, which takes into account the acceleration and rotation rate of the fixed point on the box. The equations of motion in a non-inertial frame can be derived by applying the principle of virtual work to a system of lagrangian coordinates in the non-inertial frame. This approach is known as the Non-Inertial Lagrangian formulation.