Recent content by dynamicskillingme

Sorry if I wasn't clear enough, I don't understand the concept behind the generating polynomials. My notes state the examples of the three theta methods but I can't understand how they are obtained (e.g. implicit euler is sigma(w) = w )

Hi, I'm struggling to understand how the generating polynomials work and are implemented in the difference equation for a general ODE y' = f(t,y) Difference Equation Generating polynomials "Coefficients are normalized either by a_k = 1 or sigma(1) = 1

If you could humour me as an engineer having to take a maths course and is struggling to remember concepts taught along time ago, How could I prove their answer, or what should I read up on to be able to show this proof?

Homework Statement Has solution It then goes on to state the solution blows up at , which I understand. My issue is when I do the solution I get (Working)

Okay, so I must have assumed something wrong early on or have made a pretty bad mistake in my work (not unheard of)

My Hamilton was a mess from a mistake early on. After redoing it I get . I can then formulate the hamiltonian jacobi again and get Then (and I'm mostly going from an example in my lecture notes and the question hints) I can separate the variables out as That can be substituted as In...

Homework Statement Homework EquationsThe Attempt at a Solution So far I have a solution for a) as For b) I formulate the equation as and so far for c) I have My main idea at the moment is that as the Lagrangian was not time dependent, the Hamiltonian will not be. Following on maybe...

Homework Statement Hi, I'm working on understanding how a time independent point transformation . effects the Lagrangian and to see how what values are co and contra variant.Homework Equations Would these be correct formulations, or have I overlooked something? The Attempt at a Solution and...

G is a function of q and t, (G(t,q) to be exact). Could you explain why you can change the order of the derivatives in this case?

A quick question about the same function, would be a true statement?

Oh wow, this is painful how much I overlooked that. Thanks!

correction

So for example for the euler lagrange I have

Its a mechanical system, but just working on proofs and theory so I'm working on proving how different quantities change, such as the euler lagrange equations, the generalised momenta, mechanical energy and power

Homework Statement For a gauge function G(t,q) where , does or have any alternative form or can they be expressed in any other way? Homework EquationsThe Attempt at a Solution