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[parent] cylindrical coordinate motion example of generalized coordinates (Example)

As an example let us get the equations in cylindrical coordinates

x = r cosϕ, y = rsin ϕ, z = z,

[ ] T = m- ˙r2 + r2 ˙ϕ2 + ˙z2 . 2

∂T- = m ˙r, ˙r

T--= mr ˙ϕ2, ∂r

∂T-= mr2 ˙ϕ, ∂ϕ˙

∂T- = m ˙z. ∂z˙

[ ] δ W = m ¨r − r ˙ϕ2 δr = Rδr, r

( ) δϕW = m -d r2ϕ˙ δϕ = Φrδ ϕ, dt

δzW = m ¨zδz = Z δz;

or

[ ] d2r ( dϕ )2 m --2-− r --- = R, dt dt

( ) m- d- 2d-ϕ r dt r dt = Φ,

d2z- m dt2 = Z.

"cylindrical coordinate motion example of generalized coordinates" is owned by bloftin.
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This is version 2 of cylindrical coordinate motion example of generalized coordinates, born on 2008-07-18, modified 2008-07-21.
Object id is 288, canonical name is CylindricalCoordinateMotionExampleOfGeneralizedCoordinates.
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Physics Classification: 45.20.Jj (Lagrangian and Hamiltonian mechanics)
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