Undergrad Solving 2-Body Problem w/ Lagrangian: What Substitutions?

  • Thread starter Thread starter EduardoToledo
  • Start date Start date
  • Tags Tags
    2-body Lagrangian
Click For Summary
The discussion focuses on solving the classical two-body problem using the Lagrangian principle, specifically addressing the issue of substitutions before taking partial derivatives. The original poster encountered differing results after substituting angular velocity and seeks clarification on appropriate substitutions. They suggest that substitutions involving holonomic constraints may be relevant but request a demonstration to support this. The conversation emphasizes the importance of understanding the implications of these substitutions in the context of Lagrangian mechanics. Overall, the thread aims to clarify the correct approach to substitutions in solving the two-body problem.
EduardoToledo
Messages
3
Reaction score
0
Hi, I was trying to solve the classical two body problem with Lagrangian Principle. I replaced the angular velocity before taking the partial derivatives (which respect to the distance to the virtual particle) and the result was completely different. I would like to ask, therefore, which substitutions can I do before taking these partial derivatives. I think the answer may be "the ones with holonomic constraints", but I really would like the demonstration for that
substitution in euler lagrangian equation.JPG
.
 
Physics news on Phys.org
EduardoToledo said:
I would like to ask, therefore, which substitutions can I do before taking these partial derivatives
$$q\mapsto f(t,Q),\quad \dot q\mapsto f_t+f_Q\dot Q$$
 
Thread 'What is the pressure of trapped air inside this tube?'

Thread 'What is the pressure of trapped air inside this tube?'

As you can see from the picture, i have an uneven U-shaped tube, sealed at the short end. I fill the tube with water and i seal it. So the short side is filled with water and the long side ends up containg water and trapped air. Now the tube is sealed on both sides and i turn it in such a way that the traped air moves at the short side. Are my claims about pressure in senarios A & B correct? What is the pressure for all points in senario C? (My question is basically coming from watching...
View full post »

Similar threads

Undergrad Lagrangian density of a linearly elastic string under gravity
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Instantaneous electric field solved by extended electrodynamics?
  • · Replies 1 ·
Replies
1
Views
537
Undergrad Requirement of Holonomic Constraints for Deriving Lagrange Equations
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Why isn't the Lagrangian invariant under ##\theta## rotations?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate An ab initio Hilbert space formulation of Lagrangian mechanics
  • · Replies 10 ·
Replies
10
Views
2K
Graduate Mass measurement in a Penning trap
  • · Replies 0 ·
Replies
0
Views
886
High School Why is the 3 body problem unsolvable? And what will happen if someone solves it?
  • · Replies 26 ·
Replies
26
Views
1K
Lagrangian of two body problem with spin
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Extending Hamilton's principle to systems with constraints
  • · Replies 17 ·
Replies
17
Views
3K
Graduate The Lagrangian a function of 'v' only and proving v is constant
  • · Replies 3 ·
Replies
3
Views
2K