Target angle submarine observer estimating target angle pictures himself on the target ship looking back at the submarine. Relative bearing of the submarine is the clockwise angle in degrees from the heading of the target ship to a straight line drawn from the target ship to the submarine. When target angle is 0° (or 360° ) the target ship is coming directly toward the submarine. Target angles between 0° and 90° indicate the target ship is moving toward and to the right of the submarine. Target angles between 90° and 180° indicate the target ship is moving to the right and away
Pendulum (mathematics) spring from its equilibrium position assumes the small angle approximation. The Lagrangian is then which leads to the following set of coupled differential equations: Adding and subtracting these two equations in turn, and applying the small angle approximation, gives two harmonic oscillator equations in the variables formula_61 and formula_62: with the corresponding solutions where and formula_66, formula_67, formula_47, formula_69 are constants of integration. Expressing the solutions in terms of formula_53 and formula_54 alone: If the bobs are not given an initial push, then the condition formula_73 requires formula_74, which gives (after some rearranging): Pendulum (mathematics) The mathematics of pendulums are