Ultra wide angle lens the difference is only whether distortion is present or not. However, the shorter the focal length, the more difficult it is to implement rectilinear correction. In fisheye lenses, the visual angle is close to or more than 180 degrees in at least one direction. For example, a "diagonal fish eye" would have a viewing angle of at least 180 degrees within the diagonals of the frame. A "circular fisheye" would represent the image in the form of a circle. Rectilinear ultra-wide angle lenses are used in photography and cinematography sometimes to achieve three-dimensional perspective distortion instead of simply two-dimensional barrel
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