- #1

davidwinth

- 90

- 7

Hello,

I am trying to refresh my knowledge, and so I dug out my copy of Marion and Thornton to look through. I came across an example problem, 10.2, that involves a hockey puck sliding on a flat, frictionless and rotating surface. The example problem shows some solution plots for the puck position as a function of time that were found numerically, and so I tried to code this up to see if I could get the same answers but I am stuck on how to actually code this. The puck starts out at a certain location on the rotating merry-go-round and is given an initial velocity. The idea is to find the subsequent motion.

In the example, the authors give the effective acceleration as measured by an observer on the surface as,

##a_{eff} = -\omega \times (\omega \times r) - 2\omega \times v_r##

where ##v_r## is the velocity as measured in the rotating frame and ##\omega## is constant. Performing the cross product and breaking this into Cartesian components, I get

##a_{eff} =\langle 2 \omega v_{r_y} + r \omega^2cos(\theta),-2 \omega v_{r_x} + r \omega^2sin(\theta),0 \rangle##

Can this be solved with a 2D Euler method? I have never used such a method, so before I try to figure that out I want to see if anyone knows a simpler numerical scheme to solve this, or if I am over complicating things. I think the ## v_{r_x} ## term is going to be complicated to evaluate because ## \theta ## is a function of time too.

Thanks for any input!

I am trying to refresh my knowledge, and so I dug out my copy of Marion and Thornton to look through. I came across an example problem, 10.2, that involves a hockey puck sliding on a flat, frictionless and rotating surface. The example problem shows some solution plots for the puck position as a function of time that were found numerically, and so I tried to code this up to see if I could get the same answers but I am stuck on how to actually code this. The puck starts out at a certain location on the rotating merry-go-round and is given an initial velocity. The idea is to find the subsequent motion.

In the example, the authors give the effective acceleration as measured by an observer on the surface as,

##a_{eff} = -\omega \times (\omega \times r) - 2\omega \times v_r##

where ##v_r## is the velocity as measured in the rotating frame and ##\omega## is constant. Performing the cross product and breaking this into Cartesian components, I get

##a_{eff} =\langle 2 \omega v_{r_y} + r \omega^2cos(\theta),-2 \omega v_{r_x} + r \omega^2sin(\theta),0 \rangle##

Can this be solved with a 2D Euler method? I have never used such a method, so before I try to figure that out I want to see if anyone knows a simpler numerical scheme to solve this, or if I am over complicating things. I think the ## v_{r_x} ## term is going to be complicated to evaluate because ## \theta ## is a function of time too.

Thanks for any input!

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