Solar azimuth angle be interpreted as the angle between zero and 180 degrees when the hour angle, "h", is negative (morning) and the angle between 180 and 360 degrees when the hour angle, "h", is positive (afternoon). (These two formulas are equivalent if you assume the "solar elevation angle" approximation formula). The formulas use the following terminology: Solar azimuth angle The solar azimuth angle is the azimuth angle of the Sun's position. This horizontal coordinate defines the Sun's relative direction along the local horizon, whereas the solar zenith angle (or its complementary angle solar elevation) defines the Sun's apparent altitude. There are several
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