What is Lagranage: Definition and 15 Discussions

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  1. curiousPep

    Engineering Stability Analysis of Equilibrium Solutions using Small Perturbations

    When I use Lagrange to get the equations of motion, in order to find the equilibrium conditions I set the parameters q as constants thus the derivatives to be zero and then calculate the q's that satisfy the equations of motion obtained. In ordert to check about stability I think I need to add...
  2. Abhishek11235

    Can Lagrangian Method be Applied to Solve Rocket Motion Equations?

    Homework Statement While solving equation of rocket motion with Newton's law in 1-d,I pondered to apply Lagrangian method on this. However, I didn't get correct result. Because I can eliminate last 2nd equation using last equation and get some other equation which is certainly not rockets...
  3. Phylosopher

    Bead on a Helix, angular velocity

    Homework Statement Homework Equations $$\mathcal{L}=T-U$$ $$\omega= \frac{d\phi}{dt}$$ $$I=mr^{2}$$ The Attempt at a Solution My problem is not finding the Lagrangian. But finding the kinetic energy! The translational kinetic energy would obviously be the following: $$K.E...
  4. Toby_phys

    Using Noether's Theorem to get conserved quantities

    Homework Statement N point particles of mass mα, α = 1,...,N move in their mutual gravitational field. Write down the Lagrangian for this system. Use Noether’s theorem to derive six constants of motion for the system, none of which is the energy Homework Equations Noethers Theorem: If a...
  5. A

    I Help a novice with EL equation derivation

    Hello everyone, Reading Landau and Lifshitz Course of Theoretical Physics Volume 1: Mechanics (page 3) I got suck in the following step (and I cite in italics): The change in S when q is replaced by q+δq is \int_{t_1}^{t_2} L(q+δq, \dot q +δ\dot q, t)dt - \int_{t_1}^{t_2} L(q, \dot q, t)dt...
  6. TomVu

    Finding torque from gyroscopic effect

    Hello everyone, I have a problem while calculate dynamic for gyroscope system on bicycle. I use Lagrange's equation for modelling precession effect, with generalized coordinate is a angular, the applied generalized force will be a torque. The model of gyroscope system like picture below: I've...
  7. Angelo Niforatos

    Equation of Motion for a Disk inside a Rotating Ring

    [Mentor's note : No template as this thread was moved from the technical forums] Hi all! I am working on finding the Lagrangian for the situation stated in the title. This is actually a Wolfram Mathematica demonstration as well in which they give you the Lagrangian. I am working on re-deriving...
  8. Ayenyen

    What is the tension in the strings when the slender bar begins oscillating

    Homework Statement There is a uniform slender bar which is suspended by two light inextensible strings and hangs in equilibrium. (if the mass and length of the bar are m and 2b ) Now, someone slightly knocks one end to make the bar rotate around the vertical axis with initial angular velocity...
  9. V

    I Solve Boom Crane Position with Lagrangian Equation | Wind Loading Included

    Hi, I am trying to model the position of the suspended mass at the end on a boom crane. This is basically a spherical pendulum, however further complicated by the fact that the mass can be hoisted up and down and also the pivot is connected to an arm (boom) which can be rotated up and down and...
  10. S

    Vector Field Dynamics: Apologies & Solutions

    Currently working through some exercises introducing myself to quantum field theory, however I'm completely lost with this problem. Let $$L$$ be a Lagrangian for for a real vector field $$A_\mu$$ with field strength $$F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$$ gauge parameter...
  11. 1

    1-D Lagrange and Hamilton equation gives different results.

    Homework Statement This was supposed to be an easy question. I have a question here that wants you to describe a yoyo's acceleration (in one dimension) using Lagrangian mechanics. I did and got the right answer. Now I want to use Hamilton's equations of motion but I get a wrong number. Here is...
  12. Matt atkinson

    Free Particle on spherical surface

    Homework Statement By finding the Lagrangian and using the metric: \left(\begin{array}{cc}R^2&0\\0&R^2sin^2(\theta)\end{array}\right) show that: \theta (t)=arccos(\sqrt{1-\frac{A^2}{\omega^2}}cos(\omega t +\theta_o)) Homework EquationsThe Attempt at a Solution So I got the lagrangian to be...
  13. Klas

    Lagrangian of two masses connected by a spring in semicircle

    Homework Statement Two masses are connected by a weightless spring in a friction-less semicircular well (Picture included). Derive the equations of motion with help of lagrange Homework Equations L = T - U = kinetic energy - potential energy The Attempt at a Solution ##L =...
  14. C

    Deriving Field Eqns from Gauss-Bonnet Lagrangian

    How to derive the field equations from a Gauss-Bonnet Lagrangian?
  15. Quarlep

    How does Lagrange Mechanics work in coordinate space?

    I want to know lagrange mechanics work in phase space or in coordinate system.Leonard Susskind talked about the least action and he said If we know two point we can define trajectory but I don't know the diagram that he drow its a phase space or coordinate system (x,y,z,t) 19 min or...