Inertia

Purpose

Model a rotating body with inertia

Mechanical / Rotational / Components

This component models a rotating body with inertia and two rigidly connected flanges. The angular speed is determined by the equation

\[\frac{d}{dt}\omega = \frac{1}{J}\cdot(\tau_1 + \tau_2)\]

where \(\tau_1\) and \(\tau_2\) are the torques acting at the two flanges towards the body.

Moment of inertia: The moment of inertia \(J\), in \(\left( \frac{\mathrm{kg}\cdot\mathrm{m^2}}{\mathrm{rad^2}} \right)\).

Note

Radian is a dimensionless unit, therefore, moment of inertia values in \((\mathrm{kg}\cdot\mathrm{m^2})\) and \((\mathrm{N}\cdot\mathrm{m}\cdot\mathrm{s^2})\) are also consistent with this definition.
Initial speed: The initial angular speed \(\omega_0\), in \(\left( \frac{\mathrm{rad}}{\mathrm{s}} \right)\).
Initial angle: The initial angle \(\theta_0\), in radians. May be specified in order to provide proper initial conditions if absolute angles are measured anywhere in the system. Otherwise, this parameter can be left blank.

Speed: The angular speed of the body.
Angle: The absolute angle of the body (wrapped between \(-\pi\) and \(\pi\)).