# Laplace transform of a composed function

2021-12-16

Hello,

i'm here because i didn't found anything general on this topic, i need to know what is the expression of the laplace transform a composed function like that : $$L\left \{ f(x)\circ g(x) \right \} = L\left \{ f(g(x)) \right \} = ??$$

my complete equation to transform is : $$\\ x(t)=4\times [\ddot{a}(t)cos(a(t))-\dot{a}(t)^2sin(a(t))] + 2500 \\ y(t)=4\times [-\ddot{a}(t)sin(a(t))-\dot{a}(t)^2cos(a(t))] + \frac{3.711}{4}\times t^2 + 2700$$

the goal is to isolate the $$a(t)$$ function as a function of $$x(t)$$

Thanks for your time,

Robin Luiz

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