# Lagrange_Method_example_7-2.pdf - EXAMPLE 7-2 x1 x2 y K1 y...

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K1K2K3L2L1m3m4m1m2x1x2θ1θ2yygOne can take the generalized coordinates of this system such that []Txx2121,,,θθ. Let the position vector of 3mbe +=111113cossinθθLLxx&(1.1) And the position vector of 4mbe +=222224cossinθθLLxx&(1.2) Derivations of (1.1) and (1.2) are -+=11111113sincosθθθθ±±±±&LLxx(1.3) -+=22222224sincosθθθθ±±±±&LLxx(1.4) The kinetic energy of this system is )cos2(21)cos2(212121212222222222421211111213222211412θθθθθθ±±±±±±±±±±±&LxLxmLxLxmxmxmxmTiii+++++++===(1.5) The potential energy of this system is )cos1()cos1(21)(21212241132232212211θθ-+-++-+=gLmgLmxkxxkxkV(1.6) EXAMPLE 7-2
Part I ) For the generalized coordinate 1x, )cos(11113111θθ±±±±LxmxmxT++=(1.7) 2111311131311sincos)(θθθθ±±±±±±LmLmxmmxTdtd-++=(1.8) 01=xT(1.9) )(212111xxkxk

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