equations Definition and 72 Threads

I am having a difficult time finding papers that derive the equations of motions of the Restricted Three Body Problem using Newtonian mechanics. I have found some (barely) for the CRTBP, but there are none on the ERTBP. Does it depend on what is being studied within the problem that the...

What's the root formula for fifth and higher degree polynomial equations, which have roots in radicals?

and Can someone explain how they made these equations like this? How did the radius become that equation? What formulas from algebra did they applied? I'm looking at these formulas and I don't understand how r=z+1/2*d

If I reason this as follows, I run into problems. Please help me understand what is wrong with reasoning like this. a) I start with the left hand side of the equation and let that x be -2. b) I square it. This gives me 4. So I now have the square root of 4. c) The square root of 4 is +/- 2. The...

TL;DR Summary: solve linear systems of equations Hi, I am supposed to solve the following problem with Mathematica This is the tutorial we received on how to solve linear systems with Mathematica: I then tried the whole thing for the task, but unfortunately Mathematica doesn't give me any...

Hello I have two equations given below and answer is also given solve by simultaneously i am not sure how this happen please guide thank you

I have observed that one cannot use colour here while typing something in ##\LaTeX##. Let me try : ##\text{Let's see if this can be \color{blue} {coloured}?}##. Nope, I type, via an edit after posting. Of course I can use colour from the panel above, but that will have to work for the entire...

I was given a problem to use an array, not a matrix, to solve a system of equations. I have not heard of doing this and can not find any reference to how to do it. like... 2x+3y = 12, and 3x-4y = 14 How is this solved using an array or grid?

I tried using all equations of motion but couldn't get the correct answer. Any hint would greatly help. I've tried doing this for two days now!

In circuit analysis, everything seems to work out when you set i*cos = sin. But thats not a legitimate equation, so why does that work? Is there a proof that this is a real equation?

Let $$ X \in R^{m*n} $$ where m=n with rank(X)<m then there is at-least one equation which can be written as a linear combination of other equations. Let $$ \beta \in R^{n} $$. $$ X\beta=y $$ Suppose we have x<m independent equations (the equations are consistent) formed by taking the dot...

c = fλ, where the dependent (y) variable is λ, and the independent variable (x) is f. λ = c/f c * 1/f = λ Are you able to leave 1/f as equavalent to simply 'x', where the gradient would be c, or do you have to ensure 'x'/independent variable is actually f?

I am going through https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf, here I don't understand how we wrote eq. 1.5.3 with the help of three-vectors to get eq. 1.5.4.

Euler gave us the below equations: But this doesn't actually give me a number value for where the y value is when you plug in a number for x. For example, if i plug in 2pi for x, i know cosx should be 1. But that equation gives me (e^2i*pi +e^-2i*pi)/2. This doesn't give me 1. So what really...

when is apply the formulae of resultant force for the two equations the angles cancel out and I can't get any value for the angle when i add the two equations: R^=f1^2+f2^2+2f1f2cos(theta) squart3*R=f1^2+f2^2-2f1f2cos(theta)

Hi. I have two trigonometric equations whose graphs I am trying to understand. Here are the equations: 1. a sin(x) - b cos(y) = y; a = 2, b = 2 2. a sin(x) + b cos(y) = 1; a = 1, b = 1 My question is why the graphs are the way they are. What should I do to understand them? Can anyone...

Stimulated emission-absorption have two symmetric equations for population (N_1 - number of ground state atoms, N_2 - of excited) written below, at heart of lasers: https://en.wikipedia.org/wiki/Stimulated_emission#Mathematical_model We assume that both equations act on the central target inside...

My challenge was on trying to determine the angles: My approach; came up with a number of equations: ie ##m+n=70^0## ##r=p+40^0## ##q-2r=100^0, ⇒ r=50^0 + \dfrac{1}{2} q## then it follows that, ##2q+100^0=180^0## ##⇒q=40^0, r=70^0, p=m=30^0, n=40^0## ##m+40^0+t=180^0, ⇒t=110^0## and...

I realize I can solve the other way too. But I want to solve using the equations ##v = u +at## ##S = ut +0.5(at^2)## and I don't know why I didn't get the right answer. Thank you for your help!

Please only respond if you know the node voltage method. I need to write equations for this circuit. My problem is that 1 has two paths towards 3, so when I write equations do I write both of those paths or only one. U30(1(-jXc1)+1/(jXl1+R1)+1/(jXl2)-U10((1/(-jXc1)+1/(R1+jXl1))-U20.... (the...

Are my equations correct? And my process of how I should solved this problem?

For this, Can a the equation ##x = vt + x_0## not be considered a direct proportionality between ##x## and ##v##? If so, is it because there is a constant ##x_0##? Many thanks!