COMPUTE_OUTPUT_POLAR2D

function FRC = compute_output_polar2D(rho0,psi0,stability,epsilon,Omega,W0,W1,eta,nt, saveIC, outdof)

This function computes the periodic response in full physical coordinates from reduced polar coordintes in 2D and returns the output data structure.

FRC = COMPUTE_OUTPUT_POLAR2D(rho0,psi0,stability,epsilon,Omega,W0,W1,eta,nt, saveIC, outdof)

rho0: reduced amplitude coordinate

psi0: reduced angle coordinate

stability:stability of response

epsilon: forcing amplitude

Omega: forcing frequency

W0: autonomous SSM coefficients

W1: non-autonomous SSM coefficients

eta: leading harmonic

nt: number of timesteps in periodic orbit

saveIC: whether to save full system IC for periodic orbits

outdof: DOFs at which repsonse should be computed.

FRC: full system FRC struct

See also: EXTRACT_FRC, FRC_LEVEL_SET

FRC = struct('rho', cell(numel(rho0),1), 'psi', [], 'stability', [], ...
        'Omega', [] , 'epsilon',epsilon,'Aout', [], 'Zout', [], 'Znorm', ...
        [], 'Zic', [], 'ZoutNorm', []);

    for k = 1:numel(rho0) % loop over each fixed point
        % periodic response in reduced complex coordinates
        p = polar2complex(rho0(k),psi0(k),eta,nt);

        % periodic response in Physical Coordinates
        z = reduced_to_full_traj(linspace(0,2*pi,nt),p,W0,W1,epsilon,1);

        % extract output
        [FRC(k).rho, FRC(k).psi, FRC(k).Omega, FRC(k).stability] = ...
            deal(rho0(k), psi0(k), Omega(k), stability(k));
        [FRC(k).Zout, FRC(k).Aout, FRC(k).Znorm, ...
            FRC(k).ZoutNorm] = extract_output(z, outdof);

        if saveIC
            FRC(k).Zic = z(:,1)'; % record initial condition on periodic orbit
        end
    end

end


function p = polar2complex(rho,psi,m,nt)

Complex coordinates: $\mathbf{p}(\phi)=\rho_{0}\left[\begin{array}{c}e^{\iota(\psi_{0}+m\phi)}\\e^{-\iota(\psi_{0}+m\phi)}\end{array}\right],$

phi = linspace(0,2*pi,nt);
p = rho*[exp(1i*(psi + m*phi)); exp(-1i*(psi + m*phi))];

end