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    Equations of motion of a system with non holonomic constraints

    The homework statement specifically says that the constants are non holonomic, so approaching them as holonomic would be wrong I think. Also, I didn't mention it, but it says that ##A_1, A_2, B, C## and ##D## are constants independent of the generalized coordinates. I'm not sure if it makes a...
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    Equations of motion of a system with non holonomic constraints

    Hello, I have a system with 2 degrees of freedom with 2 non-holonomic constrains that can be expressed by: ##A_1 dq_1 +Cdq_3 + Ddq_4 = 0## ##A_2 dq_1 + Bdq_2 = 0## Being ##q_1, q_2, q_3## and ##q_4## four generalized coordinates that can describe the movement of the system. And ##A_1, A_2...
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    Simple pendulum of variable mass

    Okay, thanks. I'll change my formula. Then again, can I get some sort of guidance on the solution form for the equation of motion? If mass varies slowly can I make the approximation that ##\frac {dm} {dt} \approx 0##? Or maybe assume that mass variation is constant, then: ##\frac {dm} {dt} =...
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    Simple pendulum of variable mass

    It doesn't specify anything else regarding the variable mass, just that it varies slowly in time and to consider small angles, so I think I wouldn't need to assume anything else, just that it's a variable parameter like you said, so I could use the product rule. In that case, it's correct how I...
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    Simple pendulum of variable mass

    Hello, I've got to rationally analice the form of the solutions for the equations of motion of a simple pendulum with a varying mass hanging from its thread of length ##l## (being this length constant). I approached this with lagrangian mechanics, asumming the positive ##y## direction is...
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    Calculate electric polarizability

    Hello everyone, I've got my non-uniform electric cloud distribution formula given by: ## \rho(r) = \frac {-Ze} {\pi a^3} e^{-{2r}/a}## Where ##Z## is the atomic number of the atom in question and ##a## Bohr's radius and ##E_L## the local electric field. Considering the previus expression ...
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    Normal incidence of a plane polarized wave through multiple mediums

    No worries. I found the solution on my own
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    Normal incidence of a plane polarized wave through multiple mediums

    Assuming the wave travels in direction ##z## and ##E## in direction ##x##, and ##H## in direction ##y##, putting the system reference ##z=0## at the first boundary between mediums 0 and 1, and being: ##Medium 1 = 2cm## ##Medium 2 =3 cm## ##Medium 3 = Indefinite## For mediums 0-3 (being...
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    Normal incidence of a plane polarized wave through multiple mediums

    Hello everybody, I have to find the amplitudes of a wave that goes through 4 different mediums in terms of ##E_0##, suffering reflection in the first three but not the last one. I calculated the corresponding reflection indexes of the three mediums (all of them real). Following calculations, I...
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    Phase space of a harmonic oscillator and a pendulum

    Okay, but how do I proceed to get the equations of phase space? What variables do I need to group in order to know what to draw? Also, would you know if the procedure I mentioned for the pendulum are correct?
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    Phase space of a harmonic oscillator and a pendulum

    True. Sorry about that. ##q = \sqrt{2P}A^{-1/4}\ sinQ## ##p = \sqrt{2P}A^{1/4}\ cosQ## Also, I have to apply this transformation to the Hamiltonian using ##A = Km## The resulting Hamiltonian I get is: ##H = \omega P## being ##\omega = \sqrt \frac K m## But as I said, I don't know how to...
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    Phase space of a harmonic oscillator and a pendulum

    Hello everybody, new here. Sorry in advance if I didn't follow a specific guideline to ask this. Anyways, I've got as a homework assignment two cannonical transformations (q,p)-->(Q,P). I have to obtain the hamiltonian of a harmonic oscillator, and then the new coordinates and the hamiltonian...
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