I am currently studying a maths module, as part of my second year on my physics degree, involving solutions to differential equations amongst other mathematical concepts. I have recently been (briefly) introduced to the Lorenz Equations and the idea of chaotic systems.
My question is not specifically about the Lorenz Equations, but more generally about chaotic systems.
I understand that a defining characteristic of a chaotic system is the fact that the system is extremely sensitive to its initial conditions, described simply by the notion of 'the butterfly effect'.
If I were to consider some system, such as a double pendulum, if I observed the trajectory of the pendulum over some time interval, would it in any way be possible to trace it back to its origin (i.e. its initial conditions)?
I'm not sure if I am asking a really stupid question, or if perhaps there is some theoretical/computational way to do this, or to at least estimate the initial conditions.
Thanks in advance :)