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Static problems¤

dq_10G1(q, *args) ¤

Structural static under gravity.

Source code in feniax/intrinsic/dq_static.py 
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def dq_10G1(q, *args):
    """Structural static under gravity."""

    (
        eta_0,
        gamma2,
        omega,
        phi1l,
        psi2l,
        x,
        force_gravity,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
        t,
    ) = args[0]
    X3t = postprocess.compute_strains_t(psi2l, q)
    Rab = postprocess.integrate_strainsCab(
        jnp.eye(3),
        X3t,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
    )
    F = omega * q - common.contraction_gamma2(gamma2, q)
    F += xloads.eta_pointdead(t, phi1l, x, force_gravity, Rab)
    F += eta_0
    return F

dq_10G121(q, *args) ¤

Structural static with dead point forces and gravity.

Source code in feniax/intrinsic/dq_static.py 
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def dq_10G121(q, *args):
    """Structural static with dead point forces and gravity."""

    (
        eta_0,
        gamma2,
        omega,
        phi1l,
        psi2l,
        x,
        force_dead,
        force_gravity,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
        t,
    ) = args[0]

    # @jax.jit
    def _dq_10g121(q2):
        X3t = postprocess.compute_strains_t(psi2l, q2)
        Rab = postprocess.integrate_strainsCab(
            jnp.eye(3),
            X3t,
            X_xdelta,
            C0ab,
            component_names,
            num_nodes,
            component_nodes,
            component_father,
        )
        F = omega * q2 - common.contraction_gamma2(gamma2, q2)
        F += xloads.eta_pointdead(t, phi1l, x, force_dead + force_gravity, Rab)
        F += eta_0
        return F

    F = _dq_10g121(q)
    return F

dq_10g11(q, *args) ¤

Structural static with follower point forces.

Source code in feniax/intrinsic/dq_static.py 
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def dq_10g11(q, *args):
    """Structural static with follower point forces."""

    (eta_0, gamma2, omega, phi1, x, force_follower, t) = args[0]

    # @jax.jit
    def _dq_10g11(q):
        F = omega * q - common.contraction_gamma2(gamma2, q)
        F += xloads.eta_pointfollower(t, phi1, x, force_follower)
        F += eta_0
        return F

    F = _dq_10g11(q)
    return F

dq_10g121(q, *args) ¤

Structural static with dead point forces.

Source code in feniax/intrinsic/dq_static.py 
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def dq_10g121(q, *args):
    """Structural static with dead point forces."""

    (
        eta_0,
        gamma2,
        omega,
        phi1l,
        psi2l,
        x,
        force_dead,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
        t,
    ) = args[0]

    # @jax.jit
    def _dq_10g121(q2):
        X3t = postprocess.compute_strains_t(psi2l, q2)
        Rab = postprocess.integrate_strainsCab(
            jnp.eye(3),
            X3t,
            X_xdelta,
            C0ab,
            component_names,
            num_nodes,
            component_nodes,
            component_father,
        )
        F = omega * q2 - common.contraction_gamma2(gamma2, q2)
        F += xloads.eta_pointdead(t, phi1l, x, force_dead, Rab)
        F += eta_0
        return F

    F = _dq_10g121(q)
    return F

dq_10g15(q, *args) ¤

Manoeuvre under qalpha.

Source code in feniax/intrinsic/dq_static.py 
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def dq_10g15(q, *args):
    """Manoeuvre under qalpha."""

    (eta_0, gamma2, omega, x, qalpha, A0hat, C0hat, t) = args[0]
    q0 = -q / omega
    F = omega * q - common.contraction_gamma2(gamma2, q)
    F += xloads.eta_steadyaero(q0, A0hat)
    F += xloads.eta_manoeuvre(t, x, qalpha, C0hat)
    F += eta_0
    return F

dq_11G6(q, *args) ¤

Static trim1

Source code in feniax/intrinsic/dq_static.py 
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def dq_11G6(q, *args):
    """Static trim1"""

    (
        eta_0,
        gamma2,
        omega,
        phi1,
        phi1l,
        psi2l,
        x,
        force_gravity,
        states,
        A0hat,
        B0hat,
        elevator_index,
        elevator_link,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
        t,
    ) = args[0]

    # qe = q[states['qe']]
    q2 = q[states["q2"]]
    q0i = -q2[2:] / omega[2:]
    q0 = jnp.hstack([q2[:2], q0i])
    qx = q[states["qx"]]
    X3t = postprocess.compute_strains_t(psi2l, q2)
    Rab = postprocess.integrate_strainsCab(
        jnp.eye(3),
        X3t,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
    )

    eta_gravity = xloads.eta_pointdead(t, phi1l, x, force_gravity, Rab)
    eta_aero = xloads.eta_steadyaero(q0, A0hat)
    eta_elevator = xloads.eta_controls(qx, B0hat, elevator_index, elevator_link)
    F1 = omega * q2 - common.contraction_gamma2(gamma2, q2)
    F1 += eta_gravity + eta_aero + eta_elevator
    F1 += eta_0
    Fh = phi1[:, 2, 0].dot(q0)  # added eq: 0 vertical position of first node
    # import jax.debug; jax.debug.breakpoint()
    F = jnp.hstack([F1, Fh])
    return F

dq_11G6l(q, *args) ¤

Static trim1 linear

Source code in feniax/intrinsic/dq_static.py 
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def dq_11G6l(q, *args):
    """Static trim1 linear"""

    (
        eta_0,
        omega,
        phi1,
        phi1l,
        psi2l,
        x,
        force_gravity,
        states,
        A0hat,
        B0hat,
        elevator_index,
        elevator_link,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
        t,
    ) = args[0]

    # qe = q[states['qe']]
    q2 = q[states["q2"]]
    q0i = -q2[2:] / omega[2:]
    q0 = jnp.hstack([q2[:2], q0i])
    qx = q[states["qx"]]
    X3t = postprocess.compute_strains_t(psi2l, q2)
    # Rab = postprocess.integrate_strainsCab(
    #     jnp.eye(3), X3t,
    #     X_xdelta, C0ab,
    #     component_names,
    #     num_nodes,
    #     component_nodes,
    #     component_father)

    eta_gravity = xloads.eta_pointdead(t, phi1l, x, force_gravity, C0ab)
    eta_aero = xloads.eta_steadyaero(q0, A0hat)
    eta_elevator = xloads.eta_controls(qx, B0hat, elevator_index, elevator_link)
    F1 = omega * q2  # - common.contraction_gamma2(gamma2, q2)
    F1 += eta_gravity + eta_aero + eta_elevator
    F1 += eta_0
    Fh = phi1[:, 2, 0].dot(q0)  # added eq: 0 vertical position of first node
    # import jax.debug; jax.debug.breakpoint()
    F = jnp.hstack([F1, Fh])
    return F

dq_12G2(q, *args) ¤

Static trim2

TODO: FINALISE!

Source code in feniax/intrinsic/dq_static.py 
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def dq_12G2(q, *args):
    """Static trim2

    TODO: FINALISE!
    """

    (
        eta_0,
        gamma2,
        omega,
        phi1l,
        x,
        force_gravity,
        states,
        A0hat,
        B0hat,
        C0hat,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
        t,
    ) = args[0]

    # qalpha = q[states['qalpha']]
    # qe = q[states['qe']]
    q2i = q[states["q2"]]
    q0i = -q2i / omega[2:]
    qalpha = q[states["qalpha"]]
    qx = q[states["qx"]]
    q2 = jnp.hstack([0.0, 0.0, q[states["q2"]]])
    q0 = jnp.hstack([0.0, 0.0, q0i])
    jnp.hstack([0.0, 0.0, qalpha])
    qm = jnp.hstack([0.0, 0.0, qalpha])
    eta_gravity = xloads.eta_pointdead(t, phi1l, x, force_gravity, C0ab)
    eta_aero = xloads.eta_steadyaero(q0, A0hat)
    eta_aoa = xloads.eta_manoeuvre(qm, C0hat)
    eta_elevator = xloads.eta_control(qx, B0hat)
    F = omega * q2 - common.contraction_gamma2(gamma2, q2)
    F += eta_gravity + eta_aero + eta_elevator
    F += eta_0
    return F

Dynamic problems¤

dq_20G2(t, q, *args) ¤

Free Structural dynamic gravity forces.

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20G2(t, q, *args):
    """Free Structural dynamic gravity forces."""

    (
        eta_0,
        gamma1,
        gamma2,
        omega,
        phi1l,
        psi2l,
        force_gravity,
        states,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
    ) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    qr = q[states["qr"]]

    Rab = common.computeRab_node0(
        psi2l,
        q2,
        qr,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
    )

    # no interpolation of gravity in dynamic case
    eta = xloads.eta_pointdead_const(phi1l, force_gravity[-1], Rab)
    F1, F2 = common.f_12(omega, gamma1, gamma2, q1, q2)
    F1 += eta
    F1 += eta_0
    Fr = common.f_quaternion(phi1l, q1, qr)
    F = jnp.hstack([F1, F2, Fr])
    return F

dq_20G546(t, q, *args) ¤

Free flight with gravity forces and rigid body DoF, and gust

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20G546(t, q, *args):
    """Free flight with gravity forces and rigid body DoF, and gust"""

    (
        eta_0,
        gamma1,
        gamma2,
        omega,
        phi1l,
        psi2l,
        num_modes,
        num_poles,
        A0hat,
        A1hat,
        A2hatinv,
        A3hat,
        u_inf,
        c_ref,
        poles,
        xgust,
        F1gust,
        Flgust,
        force_gravity,
        states,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
    ) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    ql = q[states["ql"]]
    q0 = q[states["q0"]]
    qr = q[states["qr"]]

    Rab = common.computeRab_node0(
        psi2l,
        q2,
        qr,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
    )

    # no interpolation of gravity in dynamic case
    eta_gravity = xloads.eta_pointdead_const(phi1l, force_gravity[-1], Rab)
    eta_aero = xloads.eta_rogerstruct(q0, q1, ql, A0hat, A1hat, num_modes, num_poles)
    eta_gust = xloads.eta_rogergust(t, xgust, F1gust)
    F1, F2 = common.f_12(omega, gamma1, gamma2, q1, q2)
    F1 += eta_aero + eta_gravity + eta_gust
    F1 += eta_0
    # jax.debug.print("time: {t}", t=t)
    # jax.debug.print("eta_aero: {eta_aero}", eta_aero=(eta_gust))
    # jax.debug.breakpoint()
    F1 = A2hatinv @ F1  # Nm
    Flgust = xloads.lags_rogergust(t, xgust, Flgust)
    Fl = xloads.lags_rogerstructure(
        A3hat, q1, ql, u_inf, c_ref, poles, num_modes, num_poles
    )  # NlxNm
    Fl += Flgust
    Fr = common.f_quaternion(phi1l, q1, qr)
    F0 = q1
    F = jnp.hstack([F1, F2, Fl, F0, Fr])
    return F

dq_20G546l(t, q, *args) ¤

Free flight with gravity forces and rigid body DoF, and gust (LINEAR)

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20G546l(t, q, *args):
    """Free flight with gravity forces and rigid body DoF, and gust
    (LINEAR)"""

    (
        eta_0,
        omega,
        phi1l,
        psi2l,
        num_modes,
        num_poles,
        A0hat,
        A1hat,
        A2hatinv,
        A3hat,
        u_inf,
        c_ref,
        poles,
        xgust,
        F1gust,
        Flgust,
        force_gravity,
        states,
        C0ab,
    ) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    ql = q[states["ql"]]
    q0 = q[states["q0"]]
    qr = q[states["qr"]]

    # Rab = common.computeRab_node0(psi2l, q2, qr, X_xdelta, C0ab,
    #                               component_names,
    #                                num_nodes,
    #                                component_nodes,
    #                                component_father)

    # no interpolation of gravity in dynamic case
    eta_gravity = xloads.eta_pointdead_const(phi1l, force_gravity[-1], C0ab)
    eta_aero = xloads.eta_rogerstruct(q0, q1, ql, A0hat, A1hat, num_modes, num_poles)
    eta_gust = xloads.eta_rogergust(t, xgust, F1gust)
    F1, F2 = common.f_12l(omega, q1, q2)
    F1 += eta_aero + eta_gravity + eta_gust
    F1 += eta_0
    # jax.debug.print("time: {t}", t=t)
    # jax.debug.print("eta_aero: {eta_aero}", eta_aero=(eta_gust))
    # jax.debug.breakpoint()
    F1 = A2hatinv @ F1  # Nm
    Flgust = xloads.lags_rogergust(t, xgust, Flgust)
    Fl = xloads.lags_rogerstructure(
        A3hat, q1, ql, u_inf, c_ref, poles, num_modes, num_poles
    )  # NlxNm
    Fl += Flgust
    Fr = common.f_quaternion(phi1l, q1, qr)
    F0 = q1
    F = jnp.hstack([F1, F2, Fl, F0, Fr])
    return F

dq_20G78(t, q, *args) ¤

Free flight with gravity forces and rigid body DoF

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20G78(t, q, *args):
    """Free flight with gravity forces and rigid body DoF"""

    (
        eta_0,
        gamma1,
        gamma2,
        omega,
        phi1l,
        psi2l,
        num_modes,
        num_poles,
        A0hat,
        A1hat,
        A2hatinv,
        A3hat,
        u_inf,
        c_ref,
        poles,
        force_gravity,
        states,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
    ) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    ql = q[states["ql"]]
    q0 = q[states["q0"]]
    qr = q[states["qr"]]

    Rab = common.computeRab_node0(
        psi2l,
        q2,
        qr,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
    )

    # no interpolation of gravity in dynamic case
    eta_gravity = xloads.eta_pointdead_const(phi1l, force_gravity[-1], Rab)
    eta_aero = xloads.eta_rogerstruct(q0, q1, ql, A0hat, A1hat, num_modes, num_poles)
    F1, F2 = common.f_12(omega, gamma1, gamma2, q1, q2)
    F1 += eta_aero + eta_gravity
    F1 += eta_0
    # jax.debug.print("time: {t}", t=t)
    # jax.debug.print("eta_aero: {eta_aero}", eta_aero=(eta_gust))
    # jax.debug.breakpoint()
    F1 = A2hatinv @ F1  # Nm
    Fl = xloads.lags_rogerstructure(
        A3hat, q1, ql, u_inf, c_ref, poles, num_modes, num_poles
    )  # NlxNm

    Fr = common.f_quaternion(phi1l, q1, qr)
    F0 = q1
    F = jnp.hstack([F1, F2, Fl, F0, Fr])
    return F

dq_20G78l(t, q, *args) ¤

Free flight with gravity forces and rigid body DoF (LINEAR)

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20G78l(t, q, *args):
    """Free flight with gravity forces and rigid body DoF (LINEAR)"""

    (
        eta_0,
        omega,
        phi1l,
        psi2l,
        num_modes,
        num_poles,
        A0hat,
        A1hat,
        A2hatinv,
        A3hat,
        u_inf,
        c_ref,
        poles,
        force_gravity,
        states,
        C0ab,
    ) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    ql = q[states["ql"]]
    q0 = q[states["q0"]]
    qr = q[states["qr"]]

    # Rab = common.computeRab_node0(psi2l, q2, qr, X_xdelta, C0ab,
    #                               component_names,
    #                                num_nodes,
    #                                component_nodes,
    #                                component_father)

    # no interpolation of gravity in dynamic case
    eta_gravity = xloads.eta_pointdead_const(phi1l, force_gravity[-1], C0ab)
    eta_aero = xloads.eta_rogerstruct(q0, q1, ql, A0hat, A1hat, num_modes, num_poles)
    F1, F2 = common.f_12l(omega, q1, q2)
    F1 += eta_aero + eta_gravity
    F1 += eta_0
    F1 = A2hatinv @ F1  # Nm
    Fl = xloads.lags_rogerstructure(
        A3hat, q1, ql, u_inf, c_ref, poles, num_modes, num_poles
    )  # NlxNm

    Fr = common.f_quaternion(phi1l, q1, qr)
    F0 = q1
    F = jnp.hstack([F1, F2, Fl, F0, Fr])
    return F

dq_20g1(t, q, *args) ¤

Clamped Structural dynamics, free vibrations.

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20g1(t, q, *args):
    """Clamped Structural dynamics, free vibrations."""

    eta_0, gamma1, gamma2, omega, states = args[0]
    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    F1, F2 = common.f_12(omega, gamma1, gamma2, q1, q2)
    F1 += eta_0
    F = jnp.hstack([F1, F2])
    return F

dq_20g11(t, q, *args) ¤

Clamped structural dynamic follower point forces.

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20g11(t, q, *args):
    """Clamped structural dynamic follower point forces."""

    (eta_0, gamma1, gamma2, omega, phi1, x, force_follower, states) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    eta = xloads.eta_pointfollower(t, phi1, x, force_follower)
    F1, F2 = common.f_12(omega, gamma1, gamma2, q1, q2)
    F1 += eta
    F1 += eta_0
    F = jnp.hstack([F1, F2])
    return F

dq_20g121(t, q, *args) ¤

Clamped structural dynamic dead point forces.

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20g121(t, q, *args):
    """Clamped structural dynamic dead point forces."""

    (
        eta_0,
        gamma1,
        gamma2,
        omega,
        phi1l,
        psi2l,
        x,
        force_dead,
        states,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
    ) = args[0]

    q1i = q[states["q1"]]
    q2i = q[states["q2"]]

    # @jax.jit
    def _dq_20g121(t, q1, q2):
        X3t = postprocess.compute_strains_t(psi2l, q2)
        Rab = postprocess.integrate_strainsCab(
            jnp.eye(3),
            X3t,
            X_xdelta,
            C0ab,
            component_names,
            num_nodes,
            component_nodes,
            component_father,
        )
        eta = xloads.eta_pointdead(t, phi1l, x, force_dead, Rab)
        F1, F2 = common.f_12(omega, gamma1, gamma2, q1, q2)
        F1 += eta
        F1 += eta_0
        F = jnp.hstack([F1, F2])
        return F

    F = _dq_20g121(t, q1i, q2i)
    return F

dq_20g2(t, q, *args) ¤

Free structural dynamic no external forces.

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20g2(t, q, *args):
    """Free structural dynamic no external forces."""

    (eta_0, gamma1, gamma2, omega, phi1l, states) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    qr = q[states["qr"]]    
    F1, F2 = common.f_12(omega, gamma1, gamma2, q1, q2)
    F1 += eta_0
    Fr = common.f_quaternion(phi1l, q1, qr)
    F = jnp.hstack([F1, F2, Fr])
    return F

dq_20g21(t, q, *args) ¤

Gust response, clamped model

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20g21(t, q, *args):
    """Gust response, clamped model"""

    (
        eta_0,
        gamma1,
        gamma2,
        omega,
        states,
        poles,        
        num_modes,
        num_poles,
        xgust,
        c_ref,
        A0hat,
        A1hat,
        A2hatinv,
        A3hat,
        u_inf,
        F1gust,
        Flgust,
    ) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    q0 = -q2 / omega
    ql = q[states["ql"]]
    # jax.debug.breakpoint()
    # ql_tensor = ql.reshape((num_modes, num_poles))
    eta_s = xloads.eta_rogerstruct(q0, q1, ql, A0hat, A1hat, num_modes, num_poles)
    eta_gust = xloads.eta_rogergust(t, xgust, F1gust)
    # jax.debug.breakpoint()
    F1, F2 = common.f_12(omega, gamma1, gamma2, q1, q2)
    F1 += eta_s + eta_gust
    F1 += eta_0
    # jax.debug.print("time: {t}", t=t)
    # jax.debug.print("eta_aero: {eta_aero}", eta_aero=(eta_gust))
    # jax.debug.breakpoint()
    F1 = A2hatinv @ F1  # Nm
    Fl = xloads.lags_rogerstructure(
        A3hat, q1, ql, u_inf, c_ref, poles, num_modes, num_poles
    )  # NlxNm
    # Fl1 = xloads.lags_rogerstructure1(A3hat, q1, ql, u_inf,
    #                                 c_ref, poles,
    #                                 num_modes, num_poles)  # NlxNm
    # Fl2 = xloads.lags_rogerstructure2(A3hat, q1, ql, u_inf,
    #                                 c_ref, poles,
    #                                 num_modes, num_poles)  # NlxNm
    # Fl = Fl1 + Fl2
    Flgust = xloads.lags_rogergust(t, xgust, Flgust)  # NlxNm
    # jax.debug.breakpoint()
    Fl += Flgust
    # jax.debug.print("eta_gust {eta_gust}", eta_gust=xgust)
    # Fl = Fl_tensor.reshape(num_modes * num_poles
    return jnp.hstack([F1, F2, Fl])

dq_20g21l(t, q, *args) ¤

Gust response.

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20g21l(t, q, *args):
    """Gust response."""

    (
        eta_0,
        omega,
        states,
        num_modes,
        num_poles,
        A0hat,
        A1hat,
        A2hatinv,
        A3hat,
        u_inf,
        c_ref,
        poles,
        xgust,
        F1gust,
        Flgust,
    ) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    q0 = -q2 / omega
    ql = q[states["ql"]]
    # jax.debug.breakpoint()
    # ql_tensor = ql.reshape((num_modes, num_poles))
    eta_s = xloads.eta_rogerstruct(q0, q1, ql, A0hat, A1hat, num_modes, num_poles)
    eta_gust = xloads.eta_rogergust(t, xgust, F1gust)
    # jax.debug.breakpoint()
    F1, F2 = common.f_12l(omega, q1, q2)
    F1 += eta_s + eta_gust
    F1 += eta_0
    # jax.debug.print("time: {t}", t=t)
    # jax.debug.print("eta_aero: {eta_aero}", eta_aero=(eta_gust))
    # jax.debug.breakpoint()
    F1 = A2hatinv @ F1  # Nm
    Fl = xloads.lags_rogerstructure(
        A3hat, q1, ql, u_inf, c_ref, poles, num_modes, num_poles
    )  # NlxNm
    # Fl1 = xloads.lags_rogerstructure1(A3hat, q1, ql, u_inf,
    #                                 c_ref, poles,
    #                                 num_modes, num_poles)  # NlxNm
    # Fl2 = xloads.lags_rogerstructure2(A3hat, q1, ql, u_inf,
    #                                 c_ref, poles,
    #                                 num_modes, num_poles)  # NlxNm
    # Fl = Fl1 + Fl2
    Flgust = xloads.lags_rogergust(t, xgust, Flgust)  # NlxNm
    # jax.debug.breakpoint()
    Fl += Flgust
    # Fl = Fl_tensor.reshape(num_modes * num_poles
    return jnp.hstack([F1, F2, Fl])

dq_20g22(t, q, *args) ¤

Free structural dynamic follower point forces.

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20g22(t, q, *args):
    """Free structural dynamic follower point forces."""

    (eta_0, gamma1, gamma2, omega, phi1, x, force_follower, states) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    eta = xloads.eta_pointfollower(t, phi1, x, force_follower)
    F1, F2 = common.f_12(omega, gamma1, gamma2, q1, q2)
    F1 += eta
    F1 += eta_0
    F = jnp.hstack([F1, F2])
    return F

dq_20g242(t, q, *args) ¤

Free Structural dynamic dead point forces.

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20g242(t, q, *args):
    """Free Structural dynamic dead point forces."""

    (
        eta_0,
        gamma1,
        gamma2,
        omega,
        phi1l,
        psi2l,
        x,
        force_dead,
        states,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
    ) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    qr = q[states["qr"]]

    Rab = common.computeRab_node0(
        psi2l,
        q2,
        qr,
        X_xdelta,
        C0ab,
        component_names,
        num_nodes,
        component_nodes,
        component_father,
    )
    eta = xloads.eta_pointdead(t, phi1l, x, force_dead, Rab)
    # import jax.debug; jax.debug.breakpoint()
    F1, F2 = common.f_12(omega, gamma1, gamma2, q1, q2)
    F1 += eta
    F1 += eta_0
    Fr = common.f_quaternion(phi1l, q1, qr)
    F = jnp.hstack([F1, F2, Fr])
    return F

dq_20g273(t, q, *args) ¤

Gust response, q0 obtained via integrator q1.

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20g273(t, q, *args):
    """Gust response, q0 obtained via integrator q1."""

    (
        eta_0,
        gamma1,
        gamma2,
        omega,
        states,
        num_modes,
        num_poles,
        A0hat,
        A1hat,
        A2hatinv,
        A3hat,
        u_inf,
        c_ref,
        poles,
        xgust,
        F1gust,
        Flgust,
    ) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    ql = q[states["ql"]]
    q0 = q[states["q0"]]
    # ql_tensor = ql.reshape((num_modes, num_poles))
    eta_s = xloads.eta_rogerstruct(q0, q1, ql, A0hat, A1hat, num_modes, num_poles)
    eta_gust = xloads.eta_rogergust(t, xgust, F1gust)
    F1, F2 = common.f_12(omega, gamma1, gamma2, q1, q2)
    F1 += eta_s + eta_gust
    F1 += eta_0
    F1 = A2hatinv @ F1  # Nm
    Fl = xloads.lags_rogerstructure(
        A3hat, q1, ql, u_inf, c_ref, poles, num_modes, num_poles
    )  # NlxNm
    Flgust = xloads.lags_rogergust(t, xgust, Flgust)  # NlxNm
    Fl += Flgust
    F0 = q1
    # Fl = Fl_tensor.reshape(num_modes * num_poles
    return jnp.hstack([F1, F2, Fl, F0])

dq_20g2gamma1(t, q, *args) ¤

Free structural dynamic no external forces.

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20g2gamma1(t, q, *args):
    """Free structural dynamic no external forces."""

    (eta_0, gamma1, omega, phi1l, states) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    qr = q[states["qr"]]
    F1, F2 = common.f_12gamma1(omega, gamma1, q1, q2)
    F1 += eta_0
    Fr = common.f_quaternion(phi1l, q1, qr)
    F = jnp.hstack([F1, F2, Fr])
    return F

dq_20g2l(t, q, *args) ¤

Free structural dynamic no external forces. Linear

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20g2l(t, q, *args):
    """Free structural dynamic no external forces. Linear"""

    (eta_0, omega, phi1l, states) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    qr = q[states["qr"]]    
    F1, F2 = common.f_12l(omega, q1, q2)
    F1 += eta_0
    Fr = common.f_quaternion(phi1l, q1, qr)
    F = jnp.hstack([F1, F2, Fr])
    return F

dq_20g546(t, q, *args) ¤

Gust response free flight, q0 obtained via integrator q1.

Source code in feniax/intrinsic/dq_dynamic.py 
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def dq_20g546(t, q, *args):
    """Gust response free flight, q0 obtained via integrator q1."""

    # (
    #     eta_0,
    #     gamma1,
    #     gamma2,
    #     omega,
    #     phi1l,
    #     states,
    #     num_modes,
    #     num_poles,
    #     A0hat,
    #     A1hat,
    #     A2hatinv,
    #     A3hat,
    #     u_inf,
    #     c_ref,
    #     poles,
    #     xgust,
    #     F1gust,
    #     Flgust,
    # ) = args[0]
    (
        eta_0,
        gamma1,
        gamma2,
        omega,
        phi1l,        
        states,
        poles,        
        num_modes,
        num_poles,
        xgust,
        c_ref,
        A0hat,
        A1hat,
        A2hatinv,
        A3hat,
        u_inf,
        F1gust,
        Flgust,
    ) = args[0]

    q1 = q[states["q1"]]
    q2 = q[states["q2"]]
    ql = q[states["ql"]]
    q0 = q[states["q0"]]
    qr = q[states["qr"]]

    # ql_tensor = ql.reshape((num_modes, num_poles))
    eta_s = xloads.eta_rogerstruct(q0, q1, ql, A0hat, A1hat, num_modes, num_poles)
    eta_gust = xloads.eta_rogergust(t, xgust, F1gust)
    F1, F2 = common.f_12(omega, gamma1, gamma2, q1, q2)
    F1 += eta_s + eta_gust
    F1 += eta_0
    F1 = A2hatinv @ F1  # Nm
    Fl = xloads.lags_rogerstructure(
        A3hat, q1, ql, u_inf, c_ref, poles, num_modes, num_poles
    )  # NlxNm
    Flgust = xloads.lags_rogergust(t, xgust, Flgust)  # NlxNm
    Fl += Flgust
    Fr = common.f_quaternion(phi1l, q1, qr)
    F0 = q1
    F = jnp.hstack([F1, F2, Fl, F0, Fr])
    return F

Helper functions¤

contraction_gamma1(gamma1, q1) ¤

Contraction of Gamma1 with velocity modal coordinate.

Parameters:

Name Type Description Default
gamma1 ndarray

3rd order tensor (NmxNmxNm) with velocity modal couplings

 required
q1 ndarray

velocity modal coordinate

 required

Returns:

Type Description
ndarray

Gamma1xq1xq1 (Nmx1)
Source code in feniax/intrinsic/dq_common.py 
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@jax.jit
def contraction_gamma1(gamma1: jnp.ndarray, q1: jnp.ndarray) -> jnp.ndarray:
    """Contraction of Gamma1 with velocity modal coordinate.

    Parameters
    ----------
    gamma1 : jnp.ndarray
        3rd order tensor (NmxNmxNm) with velocity modal couplings
    q1 : jnp.ndarray
        velocity modal coordinate

    Returns
    -------
    jnp.ndarray
        Gamma1xq1xq1 (Nmx1)
    """
    res = jnp.einsum("ijk,jk->i", gamma1, jnp.tensordot(q1, q1, axes=0))
    return res