Learning to Solve Equations of Motion with fxns dx/Sqrt[E-U(x)]

Click For Summary

Homework Help Overview

The discussion revolves around integrating equations of motion, specifically focusing on functions of the form dx/Sqrt[E-U(x)]. The original poster expresses difficulty in solving these types of integrals without relying on software tools like Mathematica, indicating a need for a method suitable for test situations.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the dependency of the integration method on the specific form of the potential function U(x). The original poster provides a specific example of U(x) and seeks advice on potential techniques for integration. Others suggest a substitution method as a possible approach.

Discussion Status

The conversation is ongoing, with participants exploring different forms of U(x) and discussing potential substitutions. There is no explicit consensus yet, but suggestions for methods are being shared.

Contextual Notes

The original poster mentions the need to solve these integrals for tests, indicating a constraint on using computational tools. The specific form of U(x) provided may also influence the discussion and approaches suggested.

nolanp2
Messages
52
Reaction score
0
i'm learning how to integrate equations of motion but can't get very far solving anything because i can't figure out how to integrate fxns of the type dx/Sqrt[E-U(x)] . The only solutions my lecturer gives me to these questions are using mathematica but i need to do them in tests so i need to find a method. can anyone help me out?
 
Physics news on Phys.org
Depends very much on the form of U(x).
 
U(x) = A[1-e^(-ax)] is there a trick to solving this?
 
It would seem obvious to me to try the substitution u= 1- e-ax.
Of course, you would then know that e-ax= 1- u.
 

Similar threads

Replies
7
Views
2K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 44 ·
2
Replies
44
Views
6K
  • · Replies 22 ·
Replies
22
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 19 ·
Replies
19
Views
2K
  • · Replies 26 ·
Replies
26
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K