brainmass.sys2nd#
- brainmass.sys2nd(A, a, u, x, v)[source]#
Second-order system dynamics.
- Implements the derivative of a second-order linear system:
d²x/dt² + 2a·dx/dt + a²·x = A·a·u
- Which can be written as:
dv/dt = A·a·u - 2·a·v - a²·x
where v = dx/dt
- Parameters:
A (
Array|ndarray|bool|number|bool|int|float|complex|Quantity) – Amplitude gain parameter.a (
Array|ndarray|bool|number|bool|int|float|complex|Quantity) – Time constant parameter (1/time).u (
Array|ndarray|bool|number|bool|int|float|complex|Quantity) – Input signal.x (
Array|ndarray|bool|number|bool|int|float|complex|Quantity) – Position state (integrated output).v (
Array|ndarray|bool|number|bool|int|float|complex|Quantity) – Velocity state (derivative of position).
- Return type:
Array|ndarray|bool|number|bool|int|float|complex|Quantity- Returns:
dv/dt - the acceleration (derivative of velocity).