Trajectory Definition and 467 Threads

I have a second order nonlinear ODE. I know that a trajectory with specified initial conditions \left[ x(0) = x_0, \dot{x}(0) = \dot{x}_0 \right] is periodic. How can I numerically calculate period of this trajectory without solve this DE?

Homework Statement In testing a missile defense system, a missile is red from the ground on a trajectory that would directly hit a bunker some distance away. When the missile is at the top of the trajectory, a laser light from the bunker ignites fuel in the missile and the missile...

hi there, new member and this is a bit off a puzzle to me (this isn't homework its something I am trying to use for a little simulation game haha) ok so the puzzle involves a ball being projected, i am wanting to find the minumum hight it can travell with the longest distance (does that make...

hello, I was just thinking since a photon trajectory is affected by a magnetic force.then I would like to know how much force does it take to do just so.

Okay, this is not a homework problem, and I think if I really played with it long enough I could work something out. But really, I just want an answer, so I'm hoping someone on here who really loves solving problems like this can just knock it out. It would be much appreciated. I'm wondering...

I wrote a game with a rocket that orbits a planet, and you can change the orbit with thrusters. As part of it I draw the predicted orbit for the rocket. To do this I compute the eccentricity vector, then the eccentricity e, then the major and minor axis of the ellipse or hyperbola as...

Homework Statement I am trying to calculate the velocity of the pendulum at the bottom of the trajectory. Mass of the ball - 2.0 kg Height - .2 m G - 9.8 m/s^2 Homework Equations PE = mgh He mentioned something about the tangential force, I'm really not sure what I should be doing...

Hello everybody :) I need some help in an experiment simulation :) If you will make a pendulum with a spring instead of a string or rope (nonelastic), then bend it over on θ angle and then let it go - it will start to oscillate around with different manner than a simple pendulum :) with...

Homework Statement Two acrobats, each of 72.0 kg, launch themselves together from a swing, holding hands. Their velocity at launch was 6.80 m/s and the angle of their initial velocity relative to the horizontal was 32.0 degrees upwards. At the top of their trajectory, their act calls for...

Homework Statement A pirate ship is on a waterfall above a fort. The height of the waterfall is 200m above the fort. The pirate captain fires a cannon with an initial velocity 40m/s at angle of 40 degrees. If the cannonball makes a direct hit on the fort, how far away(horizontally) was the...

Hi, first sorry for my bad English, I am more skilled to read than to write in English I don't know if this is the right section for this topic. The problem is described in the title of the topic. My guess is that each of the two wheels goes on with circular trajectory around a same...

Homework Statement A car is drove off a cliff at 8 m/s. it lands in the sea 3 seconds later. Homework Equations a) how far does it land? b)how high is the cliff? (g = 10m/s^2) c) at what angle relative to the horizontal does it land? The Attempt at a Solution convention chosen : upwards is...

Hi, first post here at PF :) I have a problem here regarding orbit propagation. Basically my situation is as follows: I have coded a system that can track the orbital parameters from an object in a simulated orbit (Basic rigidbody physics). The system takes the state vectors of the orbiting...

Hello, I'm trying to simulate a projectile movement (without any air friction). But my projectile parameters are not conventional. I know : The initial height (y0) The initial velocity (v0) The maximum horizontal travel distance (d) The maximum height (h) I need to find ...

In my lecture they give the phase space picture for a simple pendulum http://mathematicalgarden.files.wordpress.com/2009/03/pendulum-portrait3.png?w=500&h=195 and then say that adjacent trajectories never diverge and therefore evolution is predictable. I wanted to ask, is the statement that...

I get different result than stated in the book. What am I doing wrong? Homework Statement A spacecraft returning from a lunar mission approaches Earth on a hyperbolic trajectory. At its closest approach A it is at an altitude of 5000 km, traveling at 10 km/s. At A retrorockets are fired to...

Why is it that an electron traveling under the influence of a magnetic field (i.e electron going from left to right and B field going into the page) will travel in the arc of a circle yet when an electric field alone is applied (say up page and the direction of motion of the electron is the...

Hi guys, I have some questions about this equation that my class were given before carrying out our practical for projectile motion (what we did was release a marble from the top of an inclined ramp and then when it hits the board which has a piece of carbon paper on it, a mark is left on a...

Could one deduce mathematically the inverse-square nature of the law of gravity from measurement of the parabolic trajectory of a given projectile in earthbound flight? Could one further deduce the entire law itself from the same? IH

Homework Statement Determine the possible trajectories of a particle into the following central potential: U(r)=U_0 for r< r_0 and U(r)=0 for r>r_0.Homework Equations Not sure. What I used: Lagrangian+Euler/Lagrange equations.The Attempt at a Solution I used polar coordinates but I'm not sure...

OK, having been researching this of late, I've come to the conclusion it is far more complex than I first thought! So I guess without further ado, I'll jump into explaining my problem... Aim: Having established a set of initial conditions, I would like to be plot the trajectory of a...

I think this is a simple question but I cannot find the answer on the Internet. What trajectory would have a bullet if fired in a straight line towards space from the equator? 1- Assuming there is NO gravity involved, 2- Considering that the bullet is going at a constant velocity, 3-...

Homework Statement An anti aircraft gun with initial velocity 400m/s at angel theta above the horizontal, and the shells may be assumed to move freely under gravity. The target is a pilotless aircraft which flies at a speed of 100m/s directly towards the gun at a constant height of 3500m. A...

Hey guys, I constructed a function that describes the ballistic trajectory of an object with a given velocity and angle. This is what it looks like: y=tan(a)x+gx^2/(2(cos(a)v)^2) 'x' and 'y' are the x- and y-positions of the object in flight. 'v' is the velocity and 'a' the angle in...

Hi, I currently have this problem to solve, and I'm quite stuck. I would much appreciate it if anyone could point me in the direction on how to solve it. This is my go at it, although currently I don't have access to MATLAB until tomorrow as the university library has now closed...

Homework Statement An object is traveling N59.5E at 5.5 m/s It experiences an acceleration of 4.4 m/s^2, S76.6E for 1.5 Seconds When it ends it proceeds for 2.6 seconds with no acceleration Then is experiences a second acceleration of 4.4 m/s^2, N59.5E for 2.1 seconds I need to find out...

which is more accurate in determining the initial speed of the ball ballistic method or trajectory method??

Homework Statement A particle with mass 10kg starts from rest at r = 10 and θ=0 radians, following the trajectory given by r=10-2t , θ=0.2t. Find the radial and angular components and of the force, as functions of time, that will cause this motion Homework Equations I am unsure what...

I have an assignment where I have to build a catapult that is able to launch a bean bag any distance between 8-12 metres. My teacher will give me a random distance on the day it's due, and I have to be able to adjust the catapult in order for it to launch that distance. I'm having a bit of a...

Homework Statement A hypervelocity impact (of a meteorite or something) on a planet surface (without any atmosphere) launches fragments into hyperbolic ballistic trajectories. Assume that one of the fragments is launched with a velocity v at an angle Pi/4 from the vertical. Consider the...

I was reading an article about robotics stuff and I came across with this word "phase trajectory". I know what the phase plot is but what are trajectory and phase trajectory and is there any difference between them? Regards

I want to make a simple little video game with spaceships in it. The game only takes place in 2 dimensions, although I suspect any math would be applicable to more dimensions. The spaceships: - Have a set turning speed (radians/sec, different ships may be able to turn faster or slower) -...

Homework Statement Hello, I have an issue regarding projectile trajectory. As an assigment we have made a trebuchet, which is basically a catapult with a sling attached to it. We have done some measurements with the trebuchet itself, and have actually achievement some (according to us)...

Homework Statement http://bit.ly/eLdDK6 Look at this diagram. Given the following information, can someone help me answer the question Mass of counter weight = 760 kg Mass of projectile in arm of trebuchet = 55 kg distance of counter weight from ground = 5 m distance projectile rises...

Homework Statement Recently I met a Mathcad calculation plotting bicycle path traveled. Initial positions of tire tracks are known, their increments were calculated with bike speed 'v', wheelbase 'p', and steering angle 'a' so via ODE system solving front and rear tracks coordinates were...

I'm simulating helicopter dynamics but would like to better visualize the behavior of the helicopter and so I'm looking for some existing software solution. Ideally this would be similar to an aircraft simulator which would be rather taking position and attitude time series as input instead of...

Homework Statement You have been employed by the local circus to plan their human cannonball performace. For this act, a spring-loaded cannon will shoot a human projectile, the Great Flyinski, across the big top to a ew below. The net is located 5.0 m lower than the muzzle of the cannon from...

I'm in the process of created a computer game and I want to introduce a mortar into the game. What I want to do is given the initial position, target position, and target height, calculate the force vector that is needed to launch the mortar so it hits the target height and target distance...

Homework Statement A football player attempts a 29-yd field goal. If he is able to impart a velocity u of 95 ft/sec to the ball, compute the minimum angle θ for which the ball will clear the crossbar of the goal. The crossbar is 10 ft above the ground. (Hint: Let m = tan θ.) Homework...

If a particle's trajectory is defined by the law x=acos[pt] and y=bsin[pt] where t is parameter of time then we have to prove that it's acceleration vector passes through the focus of the conic----ellipse in this case as can be clearly seen. If we write out the position vector in the vector...

Alright, I've been working on this on my spare time for the past few weeks, and have a solution that ~works~, but I'm not happy with at all. The general idea is to have two objects, A and B, where A's velocity and position are known, B's position and speed are known, but the direction B...

Hello :-) I'am trying to figure out how to describe a trajectory of an object as a function of time. The object is a spacecraft and it sets of from Earth, travels around the moon, and then heads back to Earth...

A particle with mass 10 kg starts from rest at r=10 and theta=0 radians, following a trajectory given by r=10-2t, theta = 0.2t. Find the radial and angular components Fr and Ftheta of the force, as functions of time, that will cause this motion. Please help me get started on this problem...

**!xxx Trajectory in a gravitational field Assume an object comes from infinity and passes by the sun at 2 solar radiuses from its center. Can you derive an equation describing the objects path using only escape velocities and C??

Hello all, If there is a uniform magnetic field perpendicular to a moving charge, the charge will move in circular motion. Suppose there is a negatively charged ball with mass m in a gravity field directed downwards and a magnetic field going through the page. Since the velocity is changing...

ok. I'm a sophomore in high school who knows nothing about differential equations except for what wikipedia and some other sources said. I seem to simply have the need to figure this out. I've been to wikipedia, which didn't help. Could someone please provide a walkthrough on how to the math...

Hello! I've started working on a project that involves some light weight aircrafts. I am not a physicist(not at all) at my origin, I'm more the computer science and mathematics kind of fellow . I need to determine an aircraft trajectory form a point ( longitude and latitude ) to another taking...

Homework Statement The problem says: A motorcycle daredevil is attempting to jump across 10 buses. The takeoff ramp makes an angle theta = 18 degrees above the horizontal, and the landing ramp is identical to the take off ramp. The buses are parked side by side and each bus is 2.74m wide. The...

The formula that is applied to falling objects with disregard to any exterior forces except gravity is : d=0.5(g)(t^2) Can it also be applied to decelerating bodies, such as cars, with disregard to friction? Such as a car with an initial velocity slowing down to 0 m/s over a distance of 50...

Hello all. I need to model the trajectory of a bullet fired from a gun while being subjected to gravity, drag, and a wind vector. It's been 10yrs since my last differential equations course and I can't remember much, except enough to think that they're required to solve this problem...