- #1
beth92
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Homework Statement
For a Foucalt Pendulum:
Relative to horizontal Cartesian x and y axes fixed to the Earth (with x as East) the equations of motion for horizontal motion are:
x′′ + ω02x -2ωy′ = 0 and y′′ + ω02y + 2ωx′ = 0
[where x′, x′′, y′, y′′ are first and second time derivatives of x and y]
Convert into standard polar coordinates (ρ,φ) where x=ρcosφ and y=ρsinφ and show that:
ρ′′ + ρ(ω02-φ′2-2ωφ′) = 0
and
ρφ′′ + 2ρ′(φ′+ω) = 0
Homework Equations
The Attempt at a Solution
I'm just not sure how to convert the derivatives of x and y into polar coordinate form, eg., how to express x′ in terms of ρ′ and φ′ etc. There is no cos or sin term in the resulting equations and I'm not sure where they go...I'd appreciate some help here!