What is the Definition of p_Θ in Polar Coordinates?

[td21]

Homework Statement

What is the definition of p_Θ?

Homework Equations

I search all over the web using the keyword linear "momentum polar coordinates", "lagrangian in polar coordinates", "hamiltonian in polar coordinates", "momentum in 2D polar coordinates" for about half an hour.
but i fail to find it.

The Attempt at a Solution

I think it is either:
1. p_Θ = m*(r*d/dt(θ))^2
2. p_Θ = m*(d/dt(θ))^2

which one is correct? Thank you!

 

[BvU]

$p_\theta$ is whatever the author of the context defines it to be. Without a bit more of that context it is impossible to help you.

I find it very hard to believe you were given an exercise for which the full problem statement is actually

What is the definition of p_Θ?

Your relevant equations are not equations at all and how long you searched for them is not relevant

Neither 1 nor 2 is correct in your attempt at a solution. Is my bet.

Please start over. I do want to help, even if this reply seems a bit sour...

 

[Orodruin]

*If* you are trying to find the conjugate momentum related to the angle $\theta$ in spherical coordinates for a point mass - this is not at all clear from your post - then your alternatives cannot be right as they are quadratic in $\dot\theta$. I suggest you start from the Lagrangian in cartesian coordinates, transform it to spherical, and use the definition of the conjugate momentum.