tmdsimpy.utils.harmonic.time_series_deriv

tmdsimpy.utils.harmonic.time_series_deriv(Nt, h, X0, order)

Returns derivative of a time series defined by a set of harmonics.

Parameters:

Ntint, power of 2

Number of times considered, must be even. Must be greater than 2*h.max().

h(H,) numpy.ndarray, sorted

Harmonics considered, 0th harmonic must be first if included.

X0(Nhc, N) numpy.ndarray

Harmonic Coefficients for columns corresponding to degrees of freedom and rows corresponding to different harmonic components.

orderint

Order of the derivative returned. 0 is generally displacement, 1 is velocity, 2 is acceleration.

Returns:

x_t(Nt, N) numpy.ndarray

Time series of each DOF. Rows are time instants and columns are DOFs.

See also

tmdsimpy.jax.harmonic_utils.time_series_deriv

Implementation of this function of JAX and JIT compiled operations.

Notes

The number of harmonic components is Nhc = tmdsimpy.utils.harmonic.Nhc(h)

The normalized time instants between [0,1) for a cycle can be calculated as tau = numpy.linspace(0,1,Nt+1)[:-1].