Classical Mechanics: Finding the centripetal force acting on an object that moves within a spiral orbit.

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Homework Statement:

In polar coordinates find the force as a function of radial coordinate F(r) that allows a particle to move in logarithmic spiral orbit r=k*e^(α*θ) , where k and a are constants.

Relevant Equations:

## \frac{d^2}{dθ^2}(1/r)+1/r=(-μr^2)⋅F(r)/l^2 ##
I believe I solved this. Is this solution true? Can please anyone just check?
 

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PeroK
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Homework Statement:: In polar coordinates find the force as a function of radial coordinate F(r) that allows a particle to move in logarithmic spiral orbit r=k*e^(α*θ) , where k and a are constants.
Homework Equations:: ## \frac{d^2f}{dx^2}(1/r)+1/r=(-μr^2)⋅F(r)/l^2 ##

I believe I solved this. Is this solution true? Can please anyone just check?
The force must depend on the speed the particle is moving.
 
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The force must depend on the speed the particle is moving.
what do you mean, sir? The formula(homework equation) is given like as I wrote up there.
 
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PeroK
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what do you mean, sir? The formula(homework equation) is given like as I wrote up there.
What is the force on an object moving in a circle? It depends on ##\dot \theta##.
 
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What is the force on an object moving in a circle? It depends on ##\dot \theta##.
The formula has been corrected in the original post. Thank you!
 
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PeroK
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The formula has been corrected in the original post. Thank you!
It looks correct to me.
 

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