Main Content

Angular Units

Simscape™ implementation of angular units relies on the concept of angular units, specifically radians, being a unit but dimensionless. The notion of angular units being dimensionless is widely held in the metrology community. The fundamental angular unit, radian, is defined in the Simscape unit registry as:

pm_addunit('rad', 1, 'm/m');

which corresponds to the SI and NIST definition [1]. In other words, Simscape unit manager does not introduce a separate dimension, 'angle', with a fundamental unit of 'rad' (similar to dimensions for length or mass), but rather defines the fundamental angular unit in terms of meter over meter or, in effect, 1.

The additional angular units, degree and revolution, are defined respectively as:

pm_addunit('deg', pi/180, 'rad');
pm_addunit('rev', 2*pi, 'rad');

As a result, forward trigonometric functions, such as sin, cos, and tan, work directly with arguments expressed in angular units. For example, cosine of 90 degrees equals the cosine of (pi/2) radians and equals the cosine of (pi/2). Expansion of forward trigonometric functions works in a similar manner.

Another effect of dimensionless implementation of angular units is the convenience of the work-energy conversion. For example, torque (in N*m) multiplied by angle (in rad) can be added directly to energy (in J, or N*m). If you specify other commensurate units for the components of this equation, Simscape unit manager performs the necessary unit conversion operations and the result is the same.


[1] The NIST Reference on Constants, Units, and Uncertainty,