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Mathematical pendulum

mathematical pendulum - motion equation

Mathematical pendulum is built with massless rope with length l. One of rope’s ends is fixed to the ceiling. To the second end of rope is fixed to the material point with mass m. Material point is then hanged to the rope. When mathematical pendulum is in equilibrium material point is not moving. In equilibrium position gravity force is balanced by rope’s tension force. In a certain moment mathematical pendulum was deflected from its equilibrium and was inclined from vertical position by angle α. Mathematical pendulum is under gravity field, so gravity force works on it.

Mathematical pendulum – motion equation

State space representation

state space representation - RLC circuit example 1.
In control theory and automation engineering dynamic models of system which are often created. It is a lot of cheaper and faster to simulate something than prepare real experiment. To simulate an object behaviour the state space representation is applied. State space representation allows to examine object features when it is under influence of various extortions. Set of examples about mentioned method are placed below.

State space representation for various systems