One more question: Can F = ma be applied to the inertial acceleration vector after expressing it in E-frame components? Would this vector still be considered "inertial?"
I would think so, because it is still the same vector just expressed in a different frame, but I'd like to make sure.
Another...
Thanks for bombarding me with useless information :), it's nice to know there are other ways to do this, although I do not know of the Lagrangian techniques.
Although F = ma cannot directly be applied to the E-frame, what fictitious forces must be taken into account to solve the problem? I know...
It doesn't specify in the question whether the N frame is inertial or not, but I do need to derive the equation of motion, and the equation of motion is found by F = ma for an inertial frame of reference, right?
Am I right in thinking that technically, an inertial frame of reference is one in...
I'm trying to get the position vector of the offset mass relative to the inertial frame of reference. Do I account for the fact that the disk has rolled a little bit with respect to the inertial frame of reference? With that, I have
r,vector = d n1 + R n2 + R/2 er = R*theta n1 + R n2 + R/2 er...
I have three temperatures (temperature of the fluid going in, temperature going out, and the temperature of the surface of the tube). What I'm trying to figure out is the film temperature at which I should evaluate the flow properties. The film temperature is defined as T,f = (T,s +...
function dxdt = test(t,x)
mu = 398600.64;
dxdt_1 = x(2);
dxdt_2 = (-mu/x(1)^3)*x(1);
dxdt = [dxdt_1;dxdt_2];
It's a second-order ODE and I'm trying to solve it from the time interval of 0 to 28800. When I lower this time interval to something like 50, the program seems to work fine, but...
I'm trying to solve an ODE using matlab's ode45, but I'm receiving the following error:
Warning: Failure at t=4.509803e+01. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (1.136868e-13) at time t.
Can anybody explain what this means?
I'm trying to read more into the Lagrange-Gibbs F and G solutions for orbit determinations, but I just can't seem to find anything on it. It's in the lecture slides and in the textbook, but when I do a simple google search, I am not getting anything. The theory is correct and all, so I'm pretty...
The original Kepler equation M = E + esinE doesn't have a closed-form solution for E, like gneill just said, so approximating E is necessary.
I wrote a Matlab script for numerically approximating E via Newton-Raphson:
M = 2; e = 0.5;
E(1) = M; %initial guess
for i = 1:10
E(i+1) = E(i) -...
Ah, got it, thanks.
The function is e^2*cosM*sinM. I have two questions:
1. Why not just keep all the terms even though it's a bit more complex? Wouldn't this give better accuracy?
2. I've seen the approximation that sinx is approximated as x when x is small. But x is also small. Why don't...
Thanks, haha. It was done on paint.
I'm still having a little trouble applying the approximation that e is small.
Applying the trig identity, I have
E = M + esin(M + esinM) = M + e[ sinM*cos(esinM) + cosM*sin(esinM)].
Assuming that e is small, sin(esinM) goes to 0 and cos(esinM) = 1.
So, E = M +...
Kepler's equation: M = E - esinE, where E is to be approximated.
I'm trying to find f(e,M), a function expressed in e and M. I've tried using the trig identity sin(u + v) = sinu*cosv + cosu*sinv, but that just introduces a cosine, which I believe to be useless. Anyone with ideas?
Sorry for the confusion - the N1 labeled on the diagram is the name of one of the reference frames that I am using.
I'm not familiar with the method of Lagrangian mechanics, but I am using the Transport Theorem to relate one reference frame to another.
I wrote the inertial position vector as...