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Any of several principles that find the physical trajectory of a system by minimizing or maximizing some value computed over the proposed path (for instance geometric optics can be reproduced by insisting on a minimum time principle).
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How does $\dot{q}_i p_i - H = \dot{Q}_i P_i - K + \frac{d}{dt}F$ will give the same EL and E... [duplicate]
How does $\dot{q}_i p_i - H = \dot{Q}_i P_i - K + \frac{d}{dt}F$ give the same Euler-Lagrange equations and Equations of motion (EoM) for corresponding coordinates and allow us to determine a canonica …
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Calculus of variations -- how does it make sense to vary the position and the velocity indep...
After reading all the answers rigorously, I came up with a simple explanation. The Lagranian $L(q,\dot{q},t)$ has no notion of path, only of the values $q,\dot{q}$. At each instant "$t$", the values $ …