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This lecture covers the determination of trajectory parameters in mechanics, focusing on the simplification of the system into two equations with two unknowns. It explains how to determine the type of trajectory (circle, ellipse, parabola, or hyperbola) based on the sign of a constant. The lecture also delves into the effective potential, energy mechanics, and the application of Kepler's laws. Practical examples include analyzing the motion of the Starship Enterprise and calculating the moment of inertia of a rotating disk.