A simple qualitative physical explanation is suggested for the phenomenon of dynamic stabilization of the inverted rigid planar pendulum whose pivot is constrained to oscillate with a high frequency in the vertical direction. A quantitative theory based on the suggested approach is developed. A computer program simulating the physical system supports the analytical investigation. The simulation reveals subtle details of the motion and aids the analytical study of the subject in a manner that is mutually reinforcing.

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A simple treatment of the important old problem of the torque-induced rotation of a spinning symmetrical top is suggested. Our discussion is appropriate for teaching introductory mechanics and general physics to undergraduate students and is free from the difficulties of a traditional approach to the problem. The origin of nutation that accompanies forced precession is explained in detail, with an accent on its relationship to the torque-free precession of a symmetrical body. A small simulation program is developed that visualizes the investigated motion and illustrates its principal features. The program facilitates understanding about the counterintuitive behaviour of a gyroscope on a qualitative level.

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A detailed treatment of tide-generating forces is given, followed by a simplified dynamic theory of tidal waves. To clarify the underlying physics, we use a simple model of the ocean that consists of a water shell of uniform depth completely covering the globe. The treatment is appropriate for college and university undergraduate students studying introductory geophysics or astronomy, general physics, or intermediate mechanics. A computer simulation is developed to aid in understanding the properties of sun-or moon-induced tide-generating forces and of the stationary tidal waves created by these forces in the open ocean.