Trajectories Definition and 127 Threads

am studying a chapter on trajectories. when am given a syatem like x'=ax-bx2-cxy y'=py-qy2-rxy and they say sketch the trajectories. i know how to do it. i look for my equilibruim points, sketch the graph and check what happens maybe at x'>0 etc my problem comes when am given a matrix. how do...

Good evening, I am working my way through a JPL technical report I found online at link Specifically, I am at page 17 which looks like and I am trying to understand the relation I basically, don't understand where this relationship comes from and why it is necessary...

when you are asked to draw a trajectory for a an autonomous DE, where does one begin eg given the matrix A= 1 0 0 -1 they say find e^tA then draw the trajectories. I know how to find e^tA but i cannot draw

Homework Statement A particle moves along a trajectory with constant magnitude of the velocity |\stackrel{→}{v}|=\stackrel{→}{v0} and constant angular momentum L⃗ = L⃗0. Determine the possible trajectories. Homework Equations d(L⃗)/(dt)=\stackrel{→}{N} where \stackrel{→}{N}=torque...

Homework Statement Determine possible trajectories for particle with constant magnitude of velocity |\dot{\vec{r}}| = v0 and constant angular momentum \vec{L} = \vec{L}0 Homework Equations |\dot{\vec{r}}| = v0 \vec{L} = \vec{L}0The Attempt at a Solution I know that L dot is zero and...

Homework Statement A construction worker stands in a 2.6m deep hole, 3.1m from the edge of the hole. He tosses the hammer to a person outside the hole. If the hammer leaves his hand 1m above the bottom of the hole at an angle of 35, what is the minimum speed needed to clear the edge. Homework...

Hello ! I have to find the orthogonal trajectories of the curves : x^{2}-y^{2}=c , x^{2}+y^{2}+2cy=1 .. How can I do this?? For this: x^{2}-y^{2}=c I found \left | y \right |=\frac{M}{\left | x \right |} ,and for this: x^{2}+y^{2}+2cy=1 ,I found: y=Ax-D,c,A,D \varepsilon \Re ...

This is a fun TikZ picture to play with. \documentclass[convert = false]{standalone} \usepackage[utf8]{inputenc} % Euler for math | Palatino for rm | Helvetica for ss | Courier for tt \renewcommand{\rmdefault}{ppl} % rm...

Ok, so this is a differential equation question. How can I use the eigenvectors/eigenvalues to find the formulas for straight line trajectories and from those formulas that I come up with, how can I alter them so as to start at any given point that I would like them to (like with starter data)...

If I understand well like in kinematics where we could have eq of motion ##x=x(t)##, ##y=y(t)## and we get eq of trajectory with elimination of time. In dynamics we have ##x=x(t)##, ##p=p(t)## and with elimination of time we get eq of phase trajectory. Am I right?

Here is the question: Here is a link to the question: Find the family of functions (circles) ? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response. edit: I see the question has been deleted at Yahoo!. (Dull)

In linear algebra, you can have systems of differential equations represented by matrices. What does a "trajectory graph" of such a system show, exactly? And how can you draw one? What's the difference between such a trajectory-graph and an ordinary slope-field for a single linear...

Homework Statement I'm working on an assignment about the chaotic behaviour of the Duffing Oscillator, using Wolfram Mathematica, which has a package that can be used to calculate Lyapunov exponents. From looking the oscillator up online, I have a set of parameters that result in...

Hi answer b I forget first step 2aydy/dx = 3x^2 please can check my answer

Hi all

Referring to the diagram below, suppose the spacecraft enters the sphere of influence of Venus ($r_{\text{SOI}}$ 616000km) with a heliocentric speed of 37.7km/s and a heliocentric flight path angle $\sigma_2 = 20^{\circ}$. Suppose that the hyperbolic trajectory asymptote is designed with an...

For a long time I've wondered how you derive the equations of orbital motion from the law of universal gravitation. Recently I've been feeling like my mathematics knowledge has caught up to the point where I can attempt to do this myself, but I keep getting stuck at the same point and I was...

I am trying to understand how the Lorentz force affects bulk fluid motion when I have an applied electric field (y-axis), applied magnetic field (x-axis) and bulk fluid velocity (z-axis), all orthogonal to each other. I understand that if the fluid was at rest, an electrostatic force would...

Hi, I'm a 1st year undergrad but I left school 7 years ago! Really struggling with the physics of my course. I have some coursework to hand in for Monday but I'm a little bit stuck. I have gone over my notes and have been browsing the internet for the past hour but I don't know what to do...

Homework Statement At time t = 0, a particle is located at the point (1, 2, 3). It travels in a straight line to the point (4, 1,4), has speed 2 at (1, 2, 3) and constant acceleration 3i - j + k. Find an equation for the position vector r(t) of the particle at time t. Homework Equations The...

So I was wondering if I defined a vector field F, and a Trajectory of a particle x=t y=.5at^2+vit+si and I can find the work done by the field on a particle moving on a path with a line integral ∫F.dr, so what would this equate to for a projectile does it apply to this?, could you give me a real...

Hello all, I'm rather new to the world of computational physics and I'd just like some advice on which program I can use for plotting trajectories. I'd prefer 3D, if possible, but 2D would at least be a good start. I'm a little familiar with python, and I can get results from my .py...

Hi all, I had an exhaustive time looking on the web for software (either free or commercial) that allows someone to simulate trips into the solar system from planets. I'm looking for something that can simulate spaceship flybys in Hohman Transfer Orbits, Gravity Assists, Oberth Effects...

Bohm trajectories and "protective" measurements? I'm having trouble understanding the arguments presented in these papers. They seem to be both arguing against the de Broglie-Bohm theory bassed on the concept of "protective measurements". Is this just a rehash of the problems with the meaning...

Relationship between "Bohmian trajectories" and "Feynman paths"? Can someone summarize what (if any) relationship there is between these two? I've read that Bohmian trajectories are very different than Feynman paths but I've also come across papers suggesting that "Feynman method of summing...

Hello, I am new to this forum. I am having trouble with conceptualizing trajectories of objects. Here is a specific question that I can figure out: If a car is traveling down the hill with an incline and an object is thrown out of the car, what is the trajectory of the object? Would the...

I have recently written a trajectory program which includes aerodynamic resistance, that is, only form drag at this point. Out of curiosity I put in some ludicrous inputs such as speeds above Mach 1 (I know that wave drag becomes significant at that speed and my calculations would be rendered...

In general, how do you prove that a given trajectory in phase space is closed? For example, suppose the energy E of a one-dimensional system is given by E=\frac{1}{2}\dot{x}^2 +\frac{1}{2}x^2 + \frac{\epsilon}{4}x^4, where ε is a positive constant. Now, I can easily show that all phase...

Why do objects fall in parabolas, but things orbit in either ellipses or hyperbolas?

Homework Statement Newton's Principia suggested that if you fire a cannon from a high mountain it could fall, circle the earth, or fly away depending on how hard it was fired. Describe how this compares to bullet trajectories. What is the major difference with this trajectory? (for...

Homework Statement Q 50: The ellipse 3x2 +2y2 = 5 and y3 = x2 HINT: The curves intersect at (1,1) and (-1,1) Two families of curves are said to be orthogonal trajectories (of each other) if each member of one family is orthogonal to each member of the other family. Show that the families of...

Homework Statement A ball is launched at a speed of 10ms-1. It lands 5m away. Find the two possible values of the angle, θ, which the initial trajectory makes with the horizontal. Homework Equations The equations of motion. The Attempt at a Solution I realize that I need to find...

Homework Statement Find the orthogonal trajectories of the given family of curves: All circles through the points (1,1) and (-1,-1) I have reduced the problem to finding solutions to the following differential equation: y'=\frac{y^2-2xy-x^2+2}{y^2+2xy-x^2-2} Homework Equations...

Hello, forum! I'm a newbie here. I've been visiting this site for a while but just recently joined. Anyways, I was wondering if anyone could help with this problem. I can find the orthogonal trajectories, however, this one is killing me because there is a constant. Allow me to type it below...

The phase space trajectories of an autonomous system of equations don't intersect. Can this be proved mathematically. Also what is the physical significance of this statement. What happens if they intersect?

Homework Statement Express y'' + 5y' - 24y = 0 as a system of couple first order DEs, find the eigenvalues of the system and the nature of the critical point at the origin. As well as find the general solution to the system of coupled equations and sketch some trajectories in the phase...

In the aftermath of the recent Steinberg paper where they reconstruct average photon trajectories in the double-slit experiment, it has been pointed out several times that the reconstructed average trajectories strongly resemble the single-photon trajectories predicted by Bohmina mechanics...

I was reading Spacetime and Geometry by Caroll and I came across this notion: I have never understood this and I was wondering if someone could enlighten me.

Hi I am trying to write a code to find the minimum time until a sphere of expanding light interacts with a set of N particles moving at speed. These particles are acted on by forces which remain constant over the time period. My problem at the moment is that these particles have a mass and...

Why can't trajectories in phase space intersect?

Homework Statement Find the orthogonal trajectories of the circles x2 + y2 - ay = 0The Attempt at a Solution I differentiated the equation w.r.t. x., Replaced dy/dx with -dx/dy, Solved the equation and got xyC = y2 - x2, where C is a constant. I did not eliminate 'a' after differentiating...

Pressure -- Average Trajectories The question is this: if we have two distinct three-dimensional but hallow objects, might the average trajectory (the average distance between ANY two points on the object's surface) vary between the objects? I am lead to believe the answer is yes between a...

When a proton is fused with lithium and two alpha particles are formed, how do you know which direction they'll go. I thought they would take roughly the same path as the accelerated proton, but in the explanations of Cockroft and Walton's setup, they show the lithium at a 45 degree angle and...

Consider a dynamic system with a periodic trajectory. Given an arbitrary duration T of time, does there exist a chaotic trajectory of a similar system which approximates the closed orbit for the duration T with a given accuracy? Chaotic orbits which I've seen so far...

In relativity, can two sets of trajectories, carried out at different times, be considered equivalent if they only differ by when they change directions as they traverse their sets of trajectories? They traverse the same trajectories. The only difference is the rate at which they traverse the...

Homework Statement Show that the families (x+c1)(x2+y2)+x = 0 and (y+c2)(x2+y2)-y = 0 Homework Equations For the 2 curves to be orthogonal their slopes should be negative recriprocles. The Attempt at a Solution I'm pretty sure that for the first set of curves: y'(x) = - (2c1...

Greetings, Can photons affect each others' trajectories like other particles do when they encounter each other? Thanks

Maximum Tension and Trajectories? Homework Statement A rock of mass 3.3kg is tied to a string of length 1.2m. The rock is held at rest (at an angle of 25 degrees) so that the string is initially tight, and then it is released. (A) Find the speed of the rock when it reaches the lowest...

The set of orthogonal trajectories for the family indicated by ( x-c)^2 + y^2 = c^2 My work: y' = -(x-c)/y Since c= ( x^2 + y^2 ) / 2x plugging back in and doing -1/y' i got y' = 2xy / ( x^2 - y^2) Then I am supposed to move the x and y to a side and integrate but i don't...

Homework Statement Which of the following is the set of orthogonal trajectories for the family indicated by (x-c)^2 + y^2 = c^2 a). (x-c)^2 + y^2 = c^2 b). (x-c)^2 - y^2 = c^2 c). x^2 + (y-c)^2 = c^2 d). x^2 - (y-c)^2 = c^2 e). None of the above Homework Equations...