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Equations of motion of particle mass on parabolic surface

Given a parabolic surface $$ Z = \frac{\Omega^2}{2g}\left(X^2 + Y^2\right)$$ My textbook (Introduction to Geophysical Fluid Dynamics, 2nd ed, p.50) states: "Provided that the paraboloid is ...
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Gyrocompas equation

Ok, need a little help for part (b) of the following problem. I set my axis similar to figure 113 and have expressed both $\omega$ and $\Omega$ in terms of the new coordinates. I have been told to ...
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Trajectory the body thrown at angle to the horizon

I need to simulate some body, thrown at some angle to the horizon and at some azimuth. What would be $x(t)$, $y(t)$ and $z(t)$ involving $g(h)$, air resistance (with $\rho(h)$), Coriolis effect and ...