This question is about lipschitz continuous, i think the way to check if the solutions can be found as fixed points is just differentiating f(t), but I'm not sure about this. Can anyone give me some hints please? I will really appreciate if you can give me some small hints.
but in that case, F(f) will be -1/2,right? I am sorry but i don't really understand the hint,can you give a more specific "hint"?(i know,im bad at this)
I have already done part a and b. Part a is easy, for part b, i let the anti-derivative of f to be k(t)+c and arrive at the answer that F(f)= 1/2+ 2*k(1/2) - k(1). But i don't know how to do the next part, can anyone give me a hint? the question c ask me to show that the infimum of F is 0 and it...
Ok,this is what i currently have:
After solving the first question, i know that:
x(t)=x(0)cos(sqrt(A^2/(2w^2)-1)*t)
I know that if A^2/(2w^2)-1 is less than 0, then it is unstable, otherwise it is stable
The period seems to be 2*pi/sqrt(A^2/(2w^2)-1)
But i don't know how to find the shape of the...
Homework Equations
Theory for Kapitsa pendulum predicts that the motion consists of 2 parts:
x(t)=X(t)+ x˜(t)
(1)
With fast oscillations:
x˜(t)=−AX(t)sin(wt) /(w^2)
(2)
and a slowly varying motion X(t) which satisfies the following equation,
X''=(1−(A^2)/(2w^2))X
(3)
Homework Statement
1...