Obtain the Euler – Lagrange equationm for the extremals of the functional X2 [y2 - yy'+y²]dx X1
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![. Obtain the Euler – Lagrange equation for the extremals of the functional
X2
| [y2 - yy'+y'2 ]dlx
X1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcd52020-b8aa-45b7-bae3-dd4024ec1f3b%2Fd6178c3f-e704-4532-beb3-7751b70fa451%2F5ucjh0f_processed.png&w=3840&q=75)
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- If A=rsin(0)a, +rsin(0)a, +rsin(0)a,, determine the flux of A out of the closed surface 1D zi B. The kinetic and potential energies of the vibrating masses are T = mx{+÷mx? %3D v = }kxf+k(x2 - x)*+kx} Determine the Lagrange's Equation of Motion.If L is a Lagrangian for a system of n degrees of freedom satisfying Lagrange’s equations, show by direct substitution that L' = L + (dF(q1, ..., qn, t)/dt) also satisfies Lagrange’s equations where F is any arbitrary, but differentiable, function of its arguments.Consider an Ising model of 100 elementary dipoles. Suppose you wish to calculate the partition function for this system, using a computer that can compute one billion terms of the partition function per second. How long must you wait for the answer?Provide a written answerConsider the question of finding the points on the curve xy² = 2 closest to the origin. (a) State what function is being minimized for this problem and what the constraint is. Label each. (b) Use Lagrange multipliers to find a system of equations for finding the closest point. Write this system of equations without any vectors. Include the constraint as one of the equations. (c) Solve the system of equations from part (b) to find the points closest on the curve xy² = 2 closest to the origin.