# Lagrangian equations of motion

## Homework Statement

Find equations of motion (eom) of a particle moving in a D-dimensional flat space with the following Lagrangian

L = (1/2)mv2i - k/ra,

r = root(x2i), m,k,a are constants

## The Attempt at a Solution

The equations of motion are given by d/dt(∂L/∂vi) - ∂L/∂xi = 0

So, when I work all this out I get
ma = ka/xia+1

I have a feeling this isn;t correct though.

Am I doing the partials wrong?

## Answers and Replies

vela
Staff Emeritus
Homework Helper
Yes, you're taking the partial with respect to xi incorrectly. Try writing out the potential term in terms of the xi's and differentiating.

Also why is a multiplying m? How did the exponent of r get over there?

Yes, you're taking the partial with respect to xi incorrectly. Try writing out the potential term in terms of the xi's and differentiating.

Also why is a multiplying m? How did the exponent of r get over there?

U = k/ra = k/root(x2i)a
= k/xai
= kx-ai

Differentiating this with respect to xi gives -akx-a-1

As for the last part; sorry, when I wrote a on the LHS I was referring to the second derivative of xi w.r.t. time

vela
Staff Emeritus
Homework Helper
U = k/ra = k/root(x2i)a
= k/xai
= kx-ai

Differentiating this with respect to xi gives -akx-a-1
How are you going from k/root(x2i)a to k/xai?

Are you saying, for instance, that $\sqrt{x_1^2+x_2^2} = x_1+x_2$?

EDIT: Oh, I see why we're getting different answers. I think there's an implied summation: $$r=\sqrt{x_i^2} = \sqrt{x_i x_i} = \sqrt{\sum_i x_i^2}$$