D’Alembert’s reduction principle

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Discussion Overview

The discussion revolves around the application of D'Alembert's reduction principle to a system of equations presented as an ordinary differential equation (ODE) system. Participants are seeking clarification on the nature of the equations and the known solution.

Discussion Character

  • Debate/contested, Homework-related

Main Points Raised

  • One participant expresses confusion about how to approach the problem involving D'Alembert's principle and requests suggestions for solving it.
  • Another participant questions whether the system presented is an ODE system or an algebraic equations system and seeks clarification on the term "FS," which is later identified as "fundamental system."
  • A participant asserts that the system is indeed an ODE, while another argues that there are no derivatives present, suggesting it is not an ODE and challenges the validity of the proposed solution (t^2, -t).
  • There is a correction regarding the second equation, indicating that it should include derivatives, specifically stating that the second line should be x_2' = x_2/t^2 + 2 x_2/t.
  • A participant expresses confusion about the nature of the solution, suggesting that (t^2, -t) is a solution to the algebraic equations as written.
  • Another participant attempts to clarify the equations by rewriting them with derivatives included, indicating a potential misunderstanding in the original formulation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the system is an ODE or an algebraic system, and there is disagreement regarding the validity of the proposed solution. The discussion remains unresolved with competing views on the nature of the equations.

Contextual Notes

There are missing derivatives in the original equations as presented, and the discussion highlights the dependence on proper definitions and formulations of the equations involved.

mathrocks
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Hey guys, I'm stuck on this problem! I have no idea how to even go about solving it. I tried searching the net for D'Alembert's principle but nothing was helpful. Any suggestions on how to go about solving it will be much appreciated!

Find with the aid of D’Alembert’s reduction principle the FS of the ODE system.

x1(t)= x1(t)/t - x2(t)

x2(t)= x1(t)/t2+ 2x2(t)/2

for which a particular solution x(t)=(t2, -t) is known.
 
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Is this an ODE System or algebric equations System?

What is FS (sorry I don't know :P)?
 
elibj123 said:
Is this an ODE System or algebric equations System?

What is FS (sorry I don't know :P)?


this is an ODE. FS stands for fundamental system.
 
There are no derivatives, therefore this is not a ODE. Secondly [tex](t^2,-t)[/tex] is not a solution.
Missing derivatives, and the second line should be,
[tex]x_2' = x_2/t^2 + 2 x_2/t[/tex]
 
Last edited:
that's the point,
(t^2,-t) is the solution of the algebric equations (as he written them)
so I'm a bit confused
 
Mathrocks, do you mean
dx1(t)/dt= x1(t)/t - x2(t)

dx2(t)/dt= x1(t)/t2+ 2x2(t)/2
 

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