SHF

The SHF function evaluates a simple harmonic function at a specific value $x$ .

Format

$SHF (x, x_{0}, A, ω, ϕ, \bar{y})$

Example

<Motion_Joint
       id              = "301001"
       type            = "EXPRESSION"
       val_type        = "D"
       expr            = "SHF(TIME,0,2,2,0,0)"
       joint_id        = "10003"
       joint_type      = "R"/>

Arguments

$x$: Any valid expression used as an independent variable for the Simple Harmonic Function (SHF). For example, to use the z-displacement of I marker with respect to the J marker as resolved in the reference frame of the RM marker as the independent variable, specify $x$ as DZ({marker_i.idstring}, {marker_j.idstring}, {marker_rm.idstring}).
$x_{0}$: The independent variable offset.
$A$: The amplitude of the simple harmonic function.
$ω$: The frequency of the simple harmonic function. It is assumed to be specified in radians per unit of the independent variable unless a D is used after the value.
$ϕ$: A phase shift in the simple harmonic function. It is assumed to be in radians unless a D is used after the value.
$\bar{y}$: The average value of the simple harmonic function.

Definition

(1)

SHF = A \sin (w (x - x_{0}) - ϕ) + \bar{y}