query: How come $\frac{d}{dt}\left(\frac{\partial {r_i}}{\partial {q_j}}\right) = \frac{\partial {\dot r_i}}{\partial {q_j}}$ in Lagrangian mechanics?
positive_passages.docid: 7149
positive_passages.text: Calculus of variations -- how does it make sense to vary the position and the velocity independently?
negative_passages.docid: 45061
negative_passages.text: Physical interpretation of $Q^i = \partial _\nu T^{i \nu}$
negative_passages.docid: 109187
negative_passages.text: The differences between Lagrange and Leibniz's derivative notations
negative_passages.docid: 10953
negative_passages.text: Elementary argument for conservation laws from symmetries *without* using the Lagrangian formalism
negative_passages.docid: 4421
negative_passages.text: Proof that total derivative is the only function that can be added to Lagrangian without changing the EOM
negative_passages.docid: 85984
negative_passages.text: How come $\frac{\partial(\partial_{\beta}A_{\gamma})}{\partial(\partial_{\mu}A_{\nu})} = g_{\beta\mu}g_{\gamma\nu}$?
negative_passages.docid: 26896
negative_passages.text: Why can't $ i\hbar\frac{\partial}{\partial t}$ be considered the Hamiltonian operator?
negative_passages.docid: 29389
negative_passages.text: Why does $k/m=\omega^2$ for harmonic motion?
negative_passages.docid: 114672
negative_passages.text: Why do we use the Lagrangian and Hamiltonian instead of other related functions?
negative_passages.docid: 116612
negative_passages.text: Differential euqation for a pendulum: $ {d^2\alpha \over dt^2} + {g \over L} \cdot \alpha = 0 $
negative_passages.docid: 72906
negative_passages.text: Is $\frac{\partial}{\partial x_1}=\frac{\partial}{\partial y_1}$ if $x_1=y_1$?
negative_passages.docid: 105398
negative_passages.text: Physical intuition for higher order derivatives
negative_passages.docid: 18054
negative_passages.text: Is there a proof from the first principle that the Lagrangian L = T - V?
negative_passages.docid: 885
negative_passages.text: Why is the 2nd derivative written as $\frac{\mathrm d^2y}{\mathrm dx^2}$?
negative_passages.docid: 153727
negative_passages.text: Constant term in Lagrangian
negative_passages.docid: 123392
negative_passages.text: How does $cos(x) = \frac{\vec{v} \cdot \vec{w}}{|\vec{v}| \cdot |\vec{w}|}$ make sense?
negative_passages.docid: 155913
negative_passages.text: Lagrangian for free particle in special relativity