/// The function takes the current position, velocity, and acceleration and calculates the required jerk limited adjustment to the acceleration for the next time dt.
/// The kinematic path is constrained by :
/// maximum velocity - vel_max,
/// maximum acceleration - accel_max,
/// time constant - tc.
/// The time constant defines the acceleration error decay in the kinematic path as the system approaches constant acceleration.
/// The time constant also defines the time taken to achieve the maximum acceleration.
/// The time constant must be positive.
/// The function alters the input velocity to be the velocity that the system could reach zero acceleration in the minimum time.