A solution of equations of motion for charged particle in a uniform magnetic field are well known (##r = const##, ## \dot{\phi} = const##). But if I tring to solve this equation using only mathematical background (without physical reasoning) I can't do this due to entaglements of variables...
Homework Statement
I'd like to derive the equations of motion for a system with Lagrange density
$$\mathcal{L}= \frac{1}{2}\partial_\mu\phi\partial^\mu\phi,$$
for ##\phi:\mathcal{M}\to \mathbb{R}## a real scalar field.
Homework Equations
$$\frac{\partial...
Alright so I was just messing around with Lagrangian equation, I just learned about it, and I had gotten to this equation of motion:
Mg*sin{α} - 1.5m*x(double dot)=0
I am trying to get velocity, and my first thought was to integrate with dt, but I didn't know how to. And I'm not even sure it's...
Homework Statement
equations above are descriptive of a system with two configuration variables, q1 and q2. inputs are tau1 and tau2. d and c values are given.
the question is about conversion of above equations to a state-space equation where the state-variables are x1 = q1_dot, x2 = q1_2dot...
Homework Statement
The problem is taken from Morin's book on classical mechanics. I found out Lagrangian of motion. Now to solve, we need small angle and small x approximation. The small angle approximation is easy to treat. But how to solve small x approximation i.e how do I apply it...
So if you have a rocket lets say that discards all the structural and engine mass continuously at zero velocity that is relative to the rocket until only the payload is traveling at the final velocity - then what will the equation of motion will look like? we can neglect the drag and...
Homework Statement
This problem showed up in my final review packet, and I /think/ it should be basic kinematics, but I don't even know how to approach it with the second half of it.
An object moves according to the equation x = vt + ke^(bt), where k, v, and b are constants, x represents...
Homework Statement
I am not looking for a solution to the problem, as much as I need a clarification on what it's asking for. The problem:
"A particle of mass m slides down an inclined plane under the influence of gravity. The particle is starting its motion from rest. Find the time dependence...
Homework Statement
Andy Roberts the former West Indian Cricket player and Fast Bowler, bowled his fastest delivery in 1975 at 159.5 km/h. Neglecting air resistance, calculate the maximum distance he could have thrown the ball at this speed (on earth!) had he been able to throw it:
i)...
Homework Statement
I think I made a mistake somewhere..
Homework Equations
T = Jα
T = F*R
The Attempt at a Solution
A)
I started with T = Jα
Since there is no slip, αm = αL
Thus:
Tm / Jm = TL / JL
Plugging in, we find TL = Tm * JL / Jm = 2560
Now use T = F*R.
Tm = Fm * Rm
Plugging in...
A flying object is moving in 3D space having translational velocity and the object is also rotating. Consider a body frame (xb-yb-zb) attached to the C.G of the moving body. Hence the body attached frame is also translating and rotating (as the object is flying) with respect to a fixed inertial...
Homework Statement
A pendulum with a mass m hanging on a elastic bug rigid massless rod which may swing in the xy-plane. The pivot point is the origin of the coordinate system. The force acting on the pendulum is the sum of force of an elastic central force directed towards the origin, and...
Hi, i am an student of civil engineering and i am doing my graduate thesis. so sorry if i misspell, english is not my native languaje. so, here we go :D
Homework Statement
Before entering in details you (whoever you are) most know:
The system is scaled for obvious reasons. The system consists...
Consider the 1d motion of a body under the influence of the force given by F = -m*γ*vα. m is mass, γ is a constant of appropriate dimension, v is velocity and α is dimensionless constant. The value of α for which the motion will come to a stop in finite time is to be calculated. I solved the...
I had seen a documentary about an algorithm that uses notions of evolution to deduce the equation of motion of a system by sampling a variable connected with the system.
For example, they used the double pendulum case where they sampled the position of the free end of the pendulum and arrived...
Hi all,
I'm working on a project to control the angles of a beam(purple) with a quadcopter(orange),see figure below. The angles for both the ground-beam and beam-quadcopter will be measured with joysticks, so only roll and pitch angles will be measured and the yaw rotation is fixed.
To obtain...
Homework Statement
A projectile is launched horizontally with an initial velocity v0 from a height h. If it is assumed that there is no air resistance, which of the following expressions represents the vertical trajectory of the projectile? (A) h–gv0^2/2x^2 (B) h–gv0^2x^2 (C) h-gx^2/2v0^2 (D)...
Homework Statement
How do we find the motion equation and more specifically the motion equation of something with a mass $m$ in the vertical plane along a cylindrical path of radius $R$,
(Translation: A point of mass $m$ slides frictionless in the vertical plane along a cylindrical path of...
Homework Statement
Homework Equations
3. The Attempt at a Solution [/B]
Hello guys,I posted images since its easier to write equations.Please can someone help me check this, if this is correct so far, then i should be able to find the velocity at C, using kinetic energy?
1. Problem Statement
Assume there is an rigid object with mass m in 2D space, an impulse J = FΔt is applied at time t1 at the particle Pimp and Pimp is on the exterior boundary of the object. The impulse cause a free plane motion of the object and the object is only affected by the force of the...
Hello Physics Forums!
Supposing that we have an action that says:
$$L=\frac{1}{2}R-g_{C\bar{D}}\partial_{\mu}z^C\partial^{\mu}\bar{z}^D+\frac{1}{4} + \frac{1}{4}ImM_{IJ}F^I_{\mu\nu}\cdot F^{J\mu\nu} +\frac{1}{4}ReM_{IJ}F^I_{\mu\nu}\cdot \tilde{F}^{J\mu\nu}$$
where...
Homework Statement
what is equation of motion for pendulum?pendulum is made of pointmass, which mass is m, is fixed to thread ,which lenght is l? Oscillation aplitude is θ.Other side of thread is fixed in (0;0;0)point. at time t=0
t=0;y=0
;z=0
;φ=θ
Homework Equations...
I have a problem (this is not homework)
Based on covariant Lagrangian ## \mathcal {L} = \frac {m}{2} \frac{dx^{\mu}}{ds} \frac {dx _ {\mu}}{ds} ## record the equations of motion in Hamiltonian form for a particle in the Schwarzschild metric (SM).
Based on Legandre transformations...