I am interpreting the problem as follows: Given , find such that
But is just , so v(t) would have to equal . So in theory, could work as a "solution," but I do not think that is what the problem is intending.
Hi, I have recently been set a set of questions all of which I have been able to do apart from the last part, I just need a starting point if at all possible or some guidance. The question is as follows:
given the 2D trajectory:
r(t) = vector (x(t) y(t))
= vector (a*cos(omega*t) b*sin(omega*t))
show that r(t) can be expressed as:
r(t)=Re(Re^(i*omega*t)) where Re is the real part and R is the complex amplitude vector (X Y)
The hint is Re(z)=(z + z*)/2 to deduce what X and Y are in terms of a and b.
Ive already plotted the data and deduced that it can be expressed as:
x^2/a^2+y^2/b^2=1
Ive tried different things including working backwards and converting e^(i*omega*t) into the real and imaginary parts (a*cos(omega*t) + i*b*sin(omega*t) etc.) but to no avail. Any help would be much appreciated.
Many thanks for your reply. That is also the solution I have arrived at which I am happy enough works, I cant see where I would have gone wrong in arriving at it, however the the question states that the solutions to X and Y would be in terms of a and b and be in C (the complex numbers) which I know is technically true, but leads me to believe a different answer is required...I just don't know where I would have gone wrong. Any further help would be appreciated but many thanks for taking your time to reply.
Jamie.