Write down the Euler-Lagrange equations associated with the following Lagrangian L(t, x, y, x°, y°) : (a) x°2 + y° 2 − k 2 (x + y) 2 (b) x°2 + y° 2 − k 2 (x − y) 2 (c) x°2 + y° 2 + k 2 (x + y) 2 (d) x°2 − y° 2 + k 2 (x + y) 2

Write down the Euler-Lagrange equations associated with the following Lagrangian L(t, x, y, x°, y°) : (a) x°2 + y° 2 − k 2 (x + y) 2 (b) x°2 + y° 2 − k 2 (x − y) 2 (c) x°2 + y° 2 + k 2 (x + y) 2 (d) x°2 − y° 2 + k 2 (x + y) 2

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 36E

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Question

Question 1
Write down the Euler-Lagrange equations associated with the following Lagrangian L(t, x, y, x°, y°) :
(a) x°2 + y° 2 − k 2 (x + y) 2
(b) x°2 + y° 2 − k 2 (x − y) 2
(c) x°2 + y° 2 + k 2 (x + y) 2
(d) x°2 − y° 2 + k 2 (x + y) 2

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