Recent content by Belginator

Thanks for your advice, I didn't know about itex, and I actually made a mistake by calling the first equation a potential. It's really the first partial of the potential. But the problem otherwise remains the same, the equations are correct.

Hello! Let's say our gravitational potential is (as usual for 2 body), $$a = -\frac{\mu}{r^3} \mathbf{r}$$. Then the gradient of this is G, $$\frac{\partial G}{\partial \mathbf{r}} = G = \frac{\mu}{r^3} [3 \hat{\mathbf{r}} \hat{\mathbf{r}}^\top - I] $$ Now if we take two time derivatives of...

@ModusPwnd right I know. By simple taking the derivative you get my expression, but then there is the r-hat which is also added, but it's usually written as dauto wrote it, broken up as r-vector and mag. of r-vector. So I believe my #6 post is correct, I understand where the r-hat comes from...

Actually I think I may understand where the ##\displaystyle \mathbf{\hat{r}}_i## comes from, it's because it's a gradient, and you're taking the partials with respect to the vector components of ##\displaystyle \mathbf{r_i}##. But I'm still missing something in the original problem, I don't...

Hi dauto, I'm not sure where the ##\displaystyle \mathbf{\hat{r}_i} ## comes from, I would have said: \begin{equation} \frac{\partial}{\partial \mathbf{r}_i} \frac{1}{\| \mathbf{r}_i \|} = - \frac{1}{\| \mathbf{r}_i \|^2} \end{equation}

I see what you're saying, but I think that's making it unnecessarily complicated. I know there's a way to do it by simply keeping it in the vector form. I was originally breaking it down using the following equation: \begin{equation} \mathbf{r}_{ji} = \mathbf{r}_{i} - \mathbf{r}_{j}...

Hi guys, I'm trying to take the gradient of the potential function, and know the answer, but am not sure how to go about it. Can someone help me step by step as to how to do this. So the potential function is: \begin{equation} U = \frac{1}{2} G \sum^{N}_{i=1} \sum^{N}_{j=1,j \neq i}...

μ is actually stated as a percent of the instantaneous weight. So the frictional force: F_f = \mu mg changes as mass changes which changes the power required to keep the velocity constant. The power required to keep the constant velocity, I believe, would be exponentially decreasing, as less...

Homework Statement Hi! I seem to be having some difficulty with this one, any help would be appreciated. There is a car, assume it for simplicity to be a rectangular prism of dimensions l,w and h. The car is moving at a constant velocity v , and assume there is a drag force D = 0.5 \rho...

Hi there goral09, if you want to lift a 2-3 kg helicopter you need a minimum of 20 - 30 N of lift. Your helicopter doesn't need an acceleration capability of 9.8 m/s^2 technically as that's factored into the Weight, which is W = mg. So in order to hover your Lift needs to equal Weight (W). I...

Hi everyone, Quick question I may just not be thinking right here but I was trying to find the acceleration, velocity, and position of a rocket as a function of time. I started with acceleration: a =\frac{T}{m-\dot{m}t} - g where T is the Thrust, m is the initial mass, mdot is the mass flow...

Homework Statement Ok I have an equation: E = (1/Me)*((2/(gamma+1))*(1+((gamma-1)/2)*Me^2))^((gamma+1)/(2*gamma-2)); Where is E is a matrix of [0:1:80] and gamma is known as 1.40. What function do I use to solve for Me? I need to find a matrix of 80 values of Me each corresponding to the E...