1. ### A My T-shirt and the Standard Model

This T-shirt I bought at a physics conference displays the following equation. It looks like the Lagrangian of the Standard Model of particle physics but I only recognise lines 1 (electroweak) and 3 (Higgs mechanism). What are lines 2 and 4 and what is/isn't included? eg. are quarks, gluons...
2. ### Construct the Lagrangian for the system

Homework Statement Hello! I have some problems with constructing Lagrangian for the given system: (Attached files) Homework Equations The answer should be given in the following form: L=T-U=... The Attempt at a Solution I tried to construct the Lagrangian, but I'm not sure if I did it...
3. ### Generalized Velocity: Lagrangian

Homework Statement [/B] In this example, I know that I can define the horizontal contribution of kinetic energy to the ball as ##\frac{1}{2}m(\dot{x} + \dot{X})^2##. In the following example, Mass ##M_{x1}##'s horizontal contribution to KE is defined as ##\frac{1}{2}m(\dot{X} -...
4. ### A Difference between Hamiltonian and Lagrangian Mechanics

Hello, I am trying to "integrate into my understanding" the difference between Hamiltonian and Lagrangian mechanics. In a nutshell: If Lagrange did all the work and formulated L = T - V, they why is Hamilton's name attached to the minimization principle? YES; I KNOW about Hamilton's Second...
5. ### Lagrangian of system with circle and cube

Hello. I have some problems with making Lagrangian. I need your advice. 1. Homework Statement I have this situation: Consider the circular path is intangible and without friction. I have to find Lagrangian for coordinates x and θ. Homework Equations [/B] L = U - V The Attempt at a...
6. ### A Lagrangian of Geodesics

I've recently read in a textbook that a geodesic can be defined as the stationary point of the action \begin{align} I(\gamma)=\frac{1}{2}\int_a^b \underbrace{g(\dot{\gamma},\dot{\gamma})(s)}_{=:\mathcal{L}(\gamma,\dot{\gamma})} \mathrm{d}s \text{,} \end{align} where ##\gamma:[a,b]\rightarrow...
7. ### I The propagator and the Lagrangian

I note the following: $$\begin{split} \langle\vec{x}_n|e^{-i \frac{\mathcal{H}_n}{\hbar} (t_n-t_0)}|\vec{x}_{0}\rangle &=\delta(\vec{x}_n-\vec{x}_0)e^{-i \frac{\mathcal{H}_n}{\hbar} (t_n-t_0)} \end{split}$$ I divide the time interval as follows...
8. ### I The propagator

I note the following: \begin{split} \langle \vec{x}| \hat{U}(t-t_0) | \vec{x}_0 \rangle&=\langle \vec{x}| e^{-2 \pi i \frac{\mathcal{H}}{\hbar} (t-t_0)} | \vec{x}_0 \rangle \\ &=e^{-2 \pi i \frac{\mathcal{H}}{\hbar} (t-t_0)} \delta(\vec{x}-\vec{x}_0)...
9. ### I Two Conserved Quantities Along Geodesic

Hi Everyone! I have done three years in my undergrad in physics/math and this summer I'm doing a research project in general relativity. I generally use a computer to do my GR computations, but there is a proof that I want to do by hand and I've been having some trouble. I want to show that...
10. R

### A The Lagrangian a function of 'v' only and proving v is constant

Hi everyone. So I'm going through Landau/Lifshitz book on Mechanics and I read through a topic on inertial frames. So, because we are in an inertial frame, the Lagrangian ends up only being a function of the magnitude of the velocity only (v2) Now my question to you is, how does one prove that...
11. ### I Question from Velocity-Dependent Potential in lagrangian (Goldstein)

currently working on format.. sor i was not prepared Hi I think this question would be much related to calculus more than physics cause it seems I'd lost my way cause of calculus..... but anyway! it says, Q=- \frac{\partial{U}}{\partial{q}}+\frac{d}{dt}(\frac{\partial{U}}{ \partial{...
12. ### I Variation of perfect fluid and Lie derivative

In Hawking-Ellis Book(1973) "The large scale structure of space-time" p69-p70, they derive the energy-momentum tensor for perfect fluid by lagrangian formulation. They imply if ##D## is a sufficiently small compact region, one can represent a congruence by a diffeomorphism ##\gamma: [a,b]\times...
13. ### Example 7-10 Lagrangian Dynamics Marion and Thornton

Homework Statement A particle of mass m is on top of a frictionless hemisphere centered at the origin with radius a" Set up the lagrange equatinos determine the constraint force and the point at which the particle detaches from the hemisphere Homework Equations L=T-U The Attempt at a...
14. ### Pendulum oscillating in an accelerating car

We have a car accelerating at a uniform rate ## a ## and a pendulum of length ## l ## hanging from the ceiling ,inclined at an angle ## \phi ## to the vertical . I need to find ##\omega## for small oscillations. From the Lagrangian and Euler-Lagrange equations, the equation of motion is...

20. ### Relativistic Lagrangian

Homework Statement Show that $$\mathcal{L} = -\frac{1}{4}F^{\mu \nu}F_{\mu \nu} = - \frac{1}{2}\partial^{\mu}A^{\nu}(\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu})$$ Where $$F^{\mu \nu} = \partial^{\mu}A^{\nu} - \partial^{\nu}A^{\mu}$$ Homework Equations The Attempt at a Solution ...
21. ### I 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...
22. ### I Particle in an Electromagnetic Field

Using the Lagrangian : L = ½mv^2 - qφ + qAv What is the physical intuition of Av ? I know that A is the magnetic vector potential and that v is the velocity of the charged particle. I just don't know what their dot product means physically .
23. ### Lagrangian of 2 rotating masses on a spring, sliding down plane

Homework Statement 2 masses are connected by a spring. They are on a frictionless plane inclined relative to the horizontal by ##\alpha##. The masses are free to slide, rotate about their center of mass, and oscillate. 1. Find the Lagrangian as a sum of the Lagrangian for the COM motion and a...
24. ### Lagrangian of System

Homework Statement Uniform chain of length L is kept of a horizontal table in such a way that l of its length keeps hanging from the table. If the whole system is in equilibrium, find the Lagrangian of the system. Homework Equations Lagrangian of the system = Kinetic energy (T) - Potential...
25. ### Different formulations of the covariant EM Lagrangian

Homework Statement I'm reading through A. Zee's "Quantum Field Theory in a nutshell" for personal learning and am a bit confused about a passage he goes through when discussing field theory for the electromagnetic field. I am well versed in non relativistic quantum mechanics but have no...
26. ### A Trace in QCD lagrangian

I have a question about the use of trace in QFT in general - more specifically the use of trace in the lagrangian in the effective theory concerning chiral symmetry in QCD. I am slowly trying to get a hang of everything, and most things i am able to calculate, but i still have som very specific...
27. ### Lagrangian of two masses connected by string on inclined pln

Two masses, m1 and m2, are attached by a light string of length D. Mass m1 starts at rest on an inclined plane and mass m2 hangs as shown. The pulley is frictionless but has a moment of inertia I and radius R. Find the Lagrangian of the system and determine the acceleration of the masses using...
28. ### Lagrangian of two masses connected by a pulley on inclined p

Homework Statement Two masses, m1 and m2, are attached by a light string of length D. Mass m1 starts at rest on an inclined plane and mass m2 hangs as shown. The pulley is frictionless but has a moment of inertia I and radius R. Find the Lagrangian of the system and determine the acceleration...
29. ### Lagrangian of a double pendulum system (with a spring)

Homework Statement Find the Lagrangian for the double pendulum system given below, where the length of the massless, frictionless and non-extendable wire attaching m_1 is l. m_2 is attached to m_1 through a massless spring of constant k and length r. The spring may only stretch in the m_1-m_2...
30. ### I Special Relativity Approximation of Gravitation

Hey there, I have two questions - the first is about an approximation of a central gravitational force on a particle (of small mass) based on special relativity, and the second is about the legitimacy of a Lagrangian I'm using to calculate the motion of a particle in the Schwarzchild metric...