- #1

Hunter Bliss

- 4

- 1

## Homework Statement

(I'm learning all of this in German, so I apologize if something is translated incorrectly.) So last week we started calculus of variations, and I'm rather confused about how to approach the following problem:

The fuel consumption of a vehicle per unit of time is expressed as follows:

For what v(t) is the fuel consumption minimal and compare this consumption with another v(t) contanting a constant acceleration.

A tip is then given: Find the functional J[v] which reflects the fuel consumption and the functional for the condition. Take note that v(T) isn't given, but that the stationary J[v] implies a boundary condition of a(T) = 0.

## Homework Equations

Based on the problems we received last week, I assume y(t)+εη(t) is necessary for the minimization of this problem.

## The Attempt at a Solution

So I'm not sure how to determine the functional J(v) that reflects the fuel consumption, but I have assumed the velocity function is any sort of y(t)+εη(t) which fulfills the condition that df/dt = 0. (Which means it is extremal)

Otherwise I'm pretty lost here guys. Thanks so much for the help!

Last edited: