Purchase Solution

Change of Coordinates Lagrangian

Not what you're looking for?

Ask Custom Question

Consider a Lagrangian system, with configuration space R^n, given by (x^1, ... x^n); and Lagrangian L(x', ..., x^n; v^1, ... v^n). Now consider a new system of coordinates, (y^1,... ^n), for this same system, so the y's are functions of the x's; and, inverting, the x's are also functions of the y's. Find the Lagrangian in the y-coordinate system, and show that it produces the same physical equations of motion for the system as does the Lagrangian in the x-coordinate system.

Purchase this Solution
Solution Summary

The solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

Solution Preview

Please see attachments for complete solution.

We use the general formulas of multivariate calculus and the ...

Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Probability Quiz

Some questions on probability

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

View More Free Quizzes
Related BrainMass Solutions

  • Lagrangian of three masses and two springs

    Introduce coordinates, x1, x2 and x3 to measure their displacement from some fixed point on this axis. Express the Lagrangian of the system in terms of these coordinates and their velocities.

  • Lagrangian and Hamiltonian's Mechanics

    Use cylindrical polar coordinates and let the equation of the parabola be z=kp^2. Write down the Lagrangian in terms of p as the generalized coordinate.

  • Lagrangian of Particle Moving in Electromagnetic Field

    for this particle is: (1.5) In our specific case this turns out to be: (1.6) So the Lagrangian is: (1.7) For a Lagrangian of generalized coordinates we define a generalized momenta: (1.8) According to Euler-Lagrange equations

  • The motion of two masses and three springs

    The solution shows how to choose the generalized coordinates, develop the Lagrangian, express the equations of motion and solve them in a matrix form.

  • A particle of mass m is constrained to move on a circle of R

    In those coordinates it's easy add the Lagrange multiplier terms to the Lagrangian. First we write (1) in polar coordinates with origin the pivot point P.

  • Shortest path between two points in polar coordinates

    It can be derived in a general setting where problems are formulated in general coordinates from the Lagrangian. An important property of the Hamiltonian is that it is conserved as a function of $t$ if the Lagrangian $L$ does not depend on $t$.

  • Lagrangian equations

    choose appropriate generalized coordinates, and let the potential energy be zero at the origin. Find the Lagrangian equations of motion. Is the angular momentum about the origin conserved? Is the total energy conserved?

  • Equations of motion

    See attached file for solution The solution shows how to obtain the kinetic energy in spherical coordinates, construct the Lagrangian and derive the equation of motion of a particle moving under the influence of central potential.

  • Lagrangian for a bead in a frictionless hoop

    That is the coordinates of the bead at any time are $$ eqalign{ x(t) &= Rsinalphacosomega t,cr y(t) &= Rsinalphasinomega t,cr z(t) &= -Rcosalpha,cr } eqno(1) $$ where $R$ is the radius of the hoop and we take the bf coordinates' origin in the

View More Related Solutions