I have the following set of second-order differential equations:
eqs = {Derivative[2][x][t] +
l0 Sin[ϕ[
t]] (Sin[θ[t]] (Derivative[1][θ][t]^2 +
Derivative[1][ϕ][t]^2) -
Cos[θ[t]] Derivative[2][θ][t]) -
l0 Cos[ϕ[
t]] (2 Cos[θ[t]] Derivative[1][θ][
t] Derivative[1][ϕ][t] +
Sin[θ[t]] Derivative[2][ϕ][t]) == 0,
Derivative[2][y][t] +
l0 Cos[θ[
t]] (-2 Sin[ϕ[t]] Derivative[1][θ][
t] Derivative[1][ϕ][t] +
Cos[ϕ[t]] Derivative[2][θ][t]) -
l0 Sin[θ[
t]] (Cos[ϕ[t]] (Derivative[1][θ][t]^2 +
Derivative[1][ϕ][t]^2) +
Sin[ϕ[t]] Derivative[2][ϕ][t]) == 0,
l0 Cos[θ[t]] Derivative[1][θ][t]^2 +
Derivative[2][z][t] +
l0 Sin[θ[t]] Derivative[2][θ][t] == 0,
l0 (-g m Cos[θ[t]] -
l0 Cos[θ[t]] Sin[θ[t]] Derivative[1][ϕ][
t]^2 + Cos[θ[
t]] (-Sin[ϕ[t]] Derivative[2][x][t] +
Cos[ϕ[t]] Derivative[2][y][t]) +
Sin[θ[t]] Derivative[2][z][t] +
l0 Derivative[2][θ][t]) == 0,
l0 Sin[θ[
t]] (2 l0 Cos[θ[t]] Derivative[1][θ][
t] Derivative[1][ϕ][t] -
Cos[ϕ[t]] Derivative[2][x][t] -
Sin[ϕ[t]] Derivative[2][y][t] +
l0 Sin[θ[t]] Derivative[2][ϕ][t]) == 0};
How do I convert them into state-space form, i.e. first order differential equations? Documentation on state-space didn't help. Thanks!
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