Euler-Lagrange Expression

Related BrainMass Solutions

• The Euler-Lagrange Equation for a Variational Problem

  507779 Find the Euler-Lagrange equation for a variational problem and discuss the result.

• Functional changing variables

  Obtain the Euler-Lagrange equation corresponding to this functional. b. By changing to a new independent variable u = exp(-2x), show that the functional S[y] is equivalent to the functional (see attachment)... c.

• Calculus of variations functions

  Thank you. see attachment Solution: (a) The associated Euler-Lagrange equation is: ( 1) where (

• Geodesics of a Parabolic Cylinder

  Now the geodesics of S from r_1 to r_2 are those curves for which the Euler-Lagrange equations hold, namely: (please see the attached file) where (please see the attached file) and (please see the attached file) Now we have: (please see the

• Frictionless Train Through the Earth

  Taking care to note the nature of the integrand, write down an Euler-Lagrange equation for the extremal curve r(ϕ) [not asked to solve this]. Let a be the minimum distance of the tunnel from the center of the earth, where dr/dϕ = 0.

• Lagrangian for a Simple Pendulum

  Derive the equation of motion from the Euler-Lagrange equation, and solve for the motion in the small angle approximation. B) Assume the massless string can stretch with a restoring force F=-k(r-ro) where ro is the unstretched length.

• Finding the Minimum of a Functional

  A family of solutions is first obtained by calculating the solution to the corresponding Euler-Lagrange equation. Conditions under which the resulting two-parameter family of extremal solutions is minimal are then considered.

• Radial free fall in Schwarztchild metric.

  The action is Integral over tau of L dtau and the Euler Lagrange equations are thus: d/dtau [dL/dx^{mu}-dot] - dL/dx^{mu} = 0 You can read-off the g_{mu, nu} from the line element: ds^2 = c^2(1-2m/r)dt^2 - (1-2m/r)^(-1)dr^2 - r^2 d theta^2

• Euler Equation of Hydrodynamics

  18798 Euler Equation of Hydrodynamics Start from Euler's equation ... Take the divergence to obtain delta-p as a quadratic expression in ... Use divv = 0 to make this as simple as you can.