Equations of motion Definition and 234 Threads

  1. N

    Equations of Motion w/ spring scale

    Homework Statement http://imgur.com/a/X7mWA Homework Equations 1. ΣF = m a 2. Στ = Iθ" The Attempt at a Solution First , assuming small motion, all movement of the scale can disregard x components (so the spring stretches only in vertical direction without an impact from the x directional...
  2. O

    I Equations of motion from Born-Infeld Lagrangian

    We can write the Born-Infeld Lagrangian as: L_{BI}=1 - \sqrt{ 1+\frac{1}{2}F_{\mu\nu }F^{\mu\nu}-\frac{1}{16}\left(F_{\mu\nu}\widetilde{F}^{\mu\nu} \right)^{2}} with G^{\mu\nu}=\frac{\partial L}{\partial F_{\mu\nu}} how can we show that in empty space the equations of motion take the form...
  3. L

    Equations of Motion: Constrained Hybrid Dynamics

    Hi all, I've tried to figure this out for some time without luck. Hope you might be able to give some input. I've implemented a model-based dynamics software in MATLAB based on the works of Roy Featherstone's Springer book "Rigid Body Dynamics Algorithms". So, I have the EoM of an...
  4. Jonathan Scott

    A Reference for coordinate view of equations of motion

    Some time in the 1980s when I first started studying relativistic gravity, for ease of comparison with Newtonian and Special Relativity gravity I worked through pages of geodesic equations for a general isotropic coordinate system with spherical symmetry, converting everything to terms relating...
  5. doktorwho

    Finding the radius of curvature of trajectory

    Homework Statement The functions are given: ##r(t)=pe^{kt}## ##\theta (t)=kt## ##v(r)=\sqrt2kr## ##a(t)=2k^2r## Find the radius of the curvature of the trajectory in the function of ##r## Homework Equations $$R=\frac{(\dot x^2 + \dot y^2)^{3/2}}{(\dot x\ddot y - \ddot x\dot y)}$$ There is also...
  6. O

    Elastic Pendulum with Newton's equations of motion

    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...
  7. S

    Equations of Motion of a Mass Attached to Rotating Spring

    1. Homework Statement A particle of mass m is attached to the end of a light spring of equilibrium length a, whose other end is fixed, so that the spring is free to rotate in a horizontal plane. The tension in the spring is k times its extension. Initially the system is at rest and the...
  8. mmcsa

    Determining linear velocity of pendulum

    Hello, I'm trying to develop a pendulum to test protective equipment so I want to work out the length I'll need to generate a desired velocity and the necessary mass I'll need for a specific moment of inertia. I know there are multiple ways to solve for linear velocity with equating Ek and Ep...
  9. tomwilliam2

    Deriving equations of motion for restricted 3-body problem

    My textbook is describing a 3-body situation where there are two large masses rotating around their barycentre, and a third much smaller mass experiencing gravitational forces from the two larger masses. If the frame of reference is the one in which the barycentre is at rest, then it is not...
  10. S

    How do I see if the equations of motion are satisfied?

    Homework Statement (a) Calculate the Conserved currents $$K_{\mu \nu \alpha} $$ associated with the global lorentz transformation and express them in terms of energy momentum tensor. (b) Evaluate the currents for $$L=\frac{1}{2}\phi (\Box +m^2)\phi$$. Check that these currents satisfy...
  11. A

    Kinematics: falling stone question

    Homework Statement While standing at the edge of the roof of a building, you throw a stone upward with an initial speed of 6.91 m/s. The stone subsequently falls to the ground, which is 16.5 m below the point where the stone leaves your hand. At what speed does the stone impact the ground? How...
  12. H

    Two different equations of motion from the same Lagrangian?

    The equation of motion of a pendulum with a support oscillating horizontally sinusoidally with angular frequency ##\omega## is given by (5.116). (See attached.) I get a different answer by considering the Euler-Lagrange equation in ##x## and then eliminating ##\ddot{x}## in (5.115): Referring...
  13. I

    A Lagrangian of a monopole (Einstein notation is used)

    Hi everyone, I am trying to calculate the equation of motion of a charged particle in the field of a monopole. The magnetic field of a monopole of strength g is given by: \textbf{B} = g \frac{\textbf{r}}{r^3} And the Lagrangian by: \mathcal{L} = \frac{m\dot{\textbf{r}}^2}{2} +...
  14. S

    Equations of motion and Hamiltonian density of a massive vector field

    Homework Statement The Lagrangian density for a massive vector field ##C_{\mu}## is given by ##\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+\frac{1}{2}m^{2}C_{\mu}C^{\mu}## where ##F_{\mu\nu}=\partial_{\mu}C_{\nu}-\partial_{\nu}C_{\mu}##. Derive the equations of motion and show that when ##m...
  15. D

    A Equations of Motion for SU2 Field (Weinberg -Salam?)

    So I have the lagrangian density ## L = -\frac{1}{2} W^{\mu \nu}_i W_{\mu \nu}^i## where ##W^{\mu \nu}_i = \partial ^\mu W^\nu_i - \partial ^\nu W^\mu_i + \epsilon_i^{jk}W^\mu_j W^\nu_k## and I want to find the equations of motion. I have gotten to the stage using the EL equations...
  16. S

    How to Derive Angular Speeds and Body Frame Velocities for 4 DOF System?

    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...
  17. M

    Integrating equations of motion with Earth perturbations

    Hello to everybody, i have been programming an n-bodies integrator in MATLAB, in an earth-centric ECI perturbations framework. The main objective is to 'write down' in a procedure an interesting part of phisics, and secondly (at the very end of it) to get a complete integrator for meteor orbits...
  18. STEMucator

    Finding Analagous Electric Circuit for Mass Spring Damper System Homework

    Homework Statement Find the analogous electrical circuit for the following mass spring damper system. Homework EquationsThe Attempt at a Solution I am rusty with writing equations of motion. I wanted to see if someone could check my work. Looking at the diagram, there are three equations...
  19. Erikono

    Equations of Motion Using Newton's Method --

    Homework Statement Determine the equations of motions in terms of x and gamma. Assume small angles and that the wheel rolls without slip. The mass of the thin homogeneous large disk of radius 2R is 2m. The mass of the thin homogeneous inner disk of radius R is m. The rod of length 2R is...
  20. Erikono

    Newton's Method for Equations of Motion (Vibrations) help?

    Homework Statement Determine the equations of motions in terms of x and gamma. Assume small angles and that the wheel rolls without slip. The mass of the thin homogeneous large disk of radius 2R is 2m. The mass of the thin homogeneous inner disk of radius R is m. The rod of length 2R is...
  21. J

    D=11 supergravity equations of motion

    Quick question, I'm preparing to work on supergravity. For completeness I was deriving the equations of motion for the Bosonic sector of maximal sugra. The Action principle is ##S=\int \star R -\frac{1}{2}\star F_4\wedge F_4 + \frac{1}{6} F_4\wedge F_4\wedge A_3## with ##F_4 = dA_3##. The...
  22. V

    Three equations of motion homework

    Homework Statement Homework Equations ## 2as = v^2-u^2 ## ## v = 0 ... \text{at maximum height}## ## \therefore s = \frac{-(u)^2}{2a} \\ a = -g \\ \therefore s = \frac{-(u)^2}{-2g} = \frac{(u)^2}{2g} ## Please explain using only the Three equations of motion and not anything related to...
  23. BruceW~

    Trajectory vs. time from parametric equations of motion

    Homework Statement Sketch the trajectory over the time interval 0 ≤ t ≤ 10 of the particle whose parametric equations of motion are given by X= t−3sint . And y = 4 − 3cost find the value of x,y,t Remember that you should be in Radian mode! Answer Do you isolate the t first and plug it in...
  24. Robin04

    Equations of motion unsolvable with elementary method

    Hi, Can you help me in collecting equations of motion that are unsolvable with elementary methods (especially with high school maths)? One that I found is when I release a body attached to an ideal spring that can freely rotate around an axis. The reason why I need them is because I would like...
  25. faiziqb12

    Hi i want to derive the 2nd equation of motion using the 1st

    Homework Statement there are a lot of mathametical and graphical derivations of the three laws of motion but i have been trying to derive the second equation of motion from the first one but i always end hopeless. please help Homework Equations 1st equation v[f] = v + at 2nd...
  26. Buzz Bloom

    Equations of motion for an observer falling radially into a blackhole

    I understand that the coordinate system (CS) for a distant observer Od is different than that for an observer Of who is falling radially toward the event horizon of a non-rotating black hole (BH). Using the Schwarzschild metric, I would like to understand the transformation equations that...
  27. S

    Equations of motion two springs pendulum system

    Homework Statement Give governing equations for the system about its static equilibrium, assuming small vibrations System consists of two springs located under 45 degrees to the vertical (both have same k-value) in undisturbed situation. Lower ends of the springs are attached to each other...
  28. B

    Negative time in equations of motion

    Homework Statement My teacher keeps saying we can't have negative times because they don't exist and when I do these questions I get negatives and can't understand them at all, can someone help me? 1. How long does it take to slow a car from 10m/s to rest at a rate of -1.75m/s^2? 2.How long...
  29. B

    Constant solutions to the Lagrange equations of motion

    Homework Statement A particle moves on the surface of an inverted cone. The Lagrangian is given by Show that there is a solution of the equations of motion where and take constant values and respectively Homework Equations The equations of motion and are (1) (2) So can be...
  30. M

    Modeling Deceleration of Object Towed in Water

    So this is about a modelling project I'm doing. If you have an object that was being towed in water and the towing force is suddenly removed. There is a force F=1/2(density of fluid)(C constant)(A)V^2 that acts on the object. I am trying to find the distance X it will take for the object to...
  31. T

    Effect of a spring on equations of motion

    Homework Statement I am just wondering what effect a torsional spring, with constant K, would have on the equations (1) to (5), under the section "Force analysis and system equations". The torsional spring is located where the pendulum and cart are connected...
  32. Q

    Rotational EOM's with non diagonal inertia tensor

    I'm having difficulties understanding how I should calculate the angular velocities of a rigid body when the inertia tensor is given in body coordinates and has off diagonal elements. Let's assume I have an inertia tensor ## I = \begin{bmatrix} I_{xx} & -I_{xy} & -I_{xz} \\ -I_{yx} &...
  33. J

    Combining linear and rotational equations of motion

    I have a moving body with constant linear and rotational acceleration. Given a starting condition (position, orientation, linear and angular velocities), how can I combine the equations of motion to give a position and orientation a given time on?
  34. T

    Equations of motion for a rotational system

    Homework Statement http://postimg.org/image/9fw7awqov/ The question is to write the Laplace transformed equations of motion for the system Homework EquationsThe Attempt at a Solution I am confused about a couple of things: why is an angle is not defined for the rotation of J2. Does it means J2...
  35. F

    Equations of motion for a fixed-height inverted pendulum

    Hi everybody! I'm struggling with a physics problem I though I had solved, but as it is turning out recently, I probably hadn't. The problem might actually be pretty easy, just me being unable to solve properly. All of you are familiar with inverted pendulum. Now, imagine an inverted pendulum...
  36. P

    Finding Position from Equations of Motion at Different Times

    Usually, equations of motion (with constant acceleration) are written in terms of values of position/velocity at time ##t=0##. Take for example: $$x = x_0 + v_0t + \frac{1}{2} a t^2$$ Where ##x_0## and ##v_0## are the values (at ##t=0##) of position and velocity respectively. What if we're...
  37. G

    Structural Vibrations Analysis & Simulation

    Recently I created a structural vibrations simulation and would like to hear some feedback or suggestions.
  38. T

    Gauge Fixing Term and Equations of Motion

    Lets take QED just to simplify. When we are doing Path Integrals and we want to "fix the Gauge": 1 we add in the integral a delta(F) -meaning that we are going to integrate only in one representative of each class of equivalent configuration- 2 We take some factors out because they are constant...
  39. O

    How to Apply Rotation Constraints in a Linkage System Equation of Motion?

    Hi guys! I have a question on applying constraint on Linkage systems. Assumed that there is a two dimensional one-bar linkage, one end can only rotate and one end is free (Such as the figure above, please neglect the damper-spring system if you want). This link can rotate only 180 degrees, not...
  40. K

    Equations of Motion: When to Use & Point Object Necessity

    When can we use the three equations of motion? Also, Is it necessary for the body we are considering to be a point object?
  41. T

    How Long Does It Take for a Car to Stop with Friction After Engine Shutdown?

    Homework Statement If the engine of a car provides an acceleration of 2ms-2 to start it from rest, assuming the mass to be roughly 1000kg, calculate the time after which the car comes to rest if the engine is turned off after 15 seconds and the frictional force is 15N) Homework Equations v=u +...
  42. H

    Solve Equations of Motion: Wrench Falling Past Window

    Hey guys, I'm wondering if I can get some help with a question in my homework. Here's the question: A workman on the scaffolding outside one of the physics classrooms drops a wrench. A pupil decides to time how long it takes for it to pass the classroom window. It was found that it took...
  43. F

    Local gauge symmetries Lagrangians and equations of motion

    Hey gang, I'm re-working my way through gauge theory, and I've what may be a silly question. Promotion of global to local symmetries in order to 'reveal' gauge fields (i.e. local phase invariance + Dirac equation -> EM gauge field) is, as far as i can tell, always done on the Lagrangian...
  44. Greg Bernhardt

    What are the Hamilton equations of motion

    Definition/Summary Hamilton's equations of motion is a very general equation of a system evolving deterministically in phase space. Equations \left( {\begin{array}{*{20}{c}} {\dot q}\\ {\dot p} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 0&1\\ { - 1}&0 \end{array}}...
  45. P

    Equations of Motion Using Lagrange?

    Hi, my professor asked me to proove the equations of motion of a problem. The equations that I need to find are in page 2 of the file https://docs.google.com/file/d/0BxOdCfkh6FqpUlY5TktpbDZTc2M/edit , equations 7 and 8. But, I'm having trouble with the exercise. I uploaded my attemps...
  46. P

    Problem with Lagrange's Equations of Motion

    Hello, I have seen some pretty esoteric questions get answered pretty clearly on here so I figured I would give it a shot. I am trying to verify a derivation using Lagrange's EOM for a dynamic system and I have run into a snag with one of the terms. $$ \frac{d}{dt}(\frac{\partial...
  47. Adjoint

    A question about equations of motion under constant acceleration

    This is a very basic question. We know for a particle moving under constant acceleration we can use both the equations x = \frac{v + v_0}{2}t and x = v_0t + \frac{1}{2}at^2 If we want to find t form each of these equations, the first one gives only one value but the second one gives two...
  48. R

    Solving for Distance and Time Using Newton's Equations of Motion

    Homework Statement A bus is traveling steadily at 30 m/s along a straight road passes a stationary car which, 5s later, begins to move with a uniform acceleration of 2 m/s^2 in the same direction as the bus. (i) how long does it take the car to acquire the same speed as the bus? (ii)...
  49. E

    Finding the first integral for equations of motion

    Hi, I'm trying to find the first integral of motion for this set of PDE. I'm not really that familiar with this method of solving PDE. I'd really appreciated if someone could help me. The problem seems quite complicated but then again the paper I've got it from says it's a straigthforward...
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