In the calculus of variations, particularly Lagrangian mechanics, people often say we vary the position and the velocity independently. But velocity is the derivative of position, so how can you treat them as independent variables?
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Consider a compound pendulum pivoted about a fixed horizontal axis, illustrated by the force diagram on the right: # Okay, I can't figur...
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In the crystal, infinitesimal translational symmetry breaking makes the phonon, In ferromagnet, time-reversal symmetry breaking makes magnon...
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I was solving the sample problems for my school's IQ society and there are some I don't get. Since all I get is a final score, I wan...
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