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HomogenousCow
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I'm not entirely sure how to treat non inertial frames in the lagrangian formulation, do the normal rules still apply?
A Lagrangian in non-inertial frames is a mathematical function that describes the dynamics of a system in a non-inertial frame of reference. It takes into account the forces and accelerations present in the non-inertial frame, allowing for accurate predictions of the system's behavior.
The Lagrangian in non-inertial frames is calculated by taking into account the fictitious forces that arise in the non-inertial frame. These forces are added to the Lagrangian in the same way that real forces are added in an inertial frame.
Using a Lagrangian in non-inertial frames allows for a more general and elegant approach to solving problems in mechanics. It also takes into account the effects of non-inertial frames, which are often present in real-world situations.
Yes, a Lagrangian in non-inertial frames can be used for any system as long as the system's dynamics are described by Newton's laws of motion. This includes systems with rotational motion, variable mass, and other complex behaviors.
A Lagrangian in non-inertial frames is derived from Hamilton's principle, which states that the true motion of a system is the one that minimizes the action integral. The Lagrangian is used to calculate this integral and determine the equations of motion for the system.