Solution for Exercise 7.8 (a) The Euler-Lagrange equation is 2( )+r\'us =0 dry +

Question

Solution for Exercise 7.8 (a) The Euler-Lagrange equation is 2( )+r'us =0 dry + dy+ps-0. dx dr which expands to (b) When expressed in terms of E and g the functional is dx)3 Now change variables, az,--Ay, If 2-1 the functional is invariant, see the definition 7.1 (page 201). Now set a = 1 + and work to first order in , so = 1-5/2 and, from equation 7.13, r, -y/2. The first-integral, equation 7.15 (page 203) becomes 4 How do we fnd outandY where e is a constant. This becomes we set Fiot orcker 2.

Explanation / Answer

This solution is based on the relations given by the defintion of 7.1(as i have observed)... hope the procedure for the solution is clear for you, and i have given two questions here..

1.why do we set alpha =1+ delta??

the solution might be,, for easy calculations or to find the values of phi = x, and si=-y/2 (forgive me if you can understand the symbols names i wrote, I mensioned as i use them) from equation 7.13.

2. how do we findout phi and si??

we dont answer this question till we know the equation 7.13, first refer equation 7.13, and observe, then you will get to know how to find them.. if you have any doubt in that equation 7.13, comment me.. and i'l help you....

By your rough work... I hope this problem is clear for you....

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