D’Alembert’s reduction principle

In summary, the conversation discusses the use of D'Alembert's reduction principle to find the fundamental system (FS) of an ODE system, specifically one with equations involving x1(t) and x2(t). The speaker is stuck on how to solve the problem and asks for suggestions from others. They also clarify that FS stands for fundamental system and question whether this is an ODE system or an algebraic equations system. The conversation ends with some confusion and a request for clarification on the equations.
  • #1
mathrocks
106
0
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.
 
Physics news on Phys.org
  • #2
Is this an ODE System or algebric equations System?

What is FS (sorry I don't know :P)?
 
  • #3
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.
 
  • #4
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:
  • #5
that's the point,
(t^2,-t) is the solution of the algebric equations (as he written them)
so I'm a bit confused
 
  • #6
Mathrocks, do you mean
dx1(t)/dt= x1(t)/t - x2(t)

dx2(t)/dt= x1(t)/t2+ 2x2(t)/2
 

What is D'Alembert's reduction principle?

D'Alembert's reduction principle is a mathematical concept used in mechanics to determine the equations of motion for a system of particles or rigid bodies. It states that the sum of the applied forces and inertial forces acting on a system must be equal to the total mass of the system times its acceleration.

How does D'Alembert's reduction principle simplify the equations of motion?

D'Alembert's reduction principle allows for the elimination of the unknown constraint forces in a system, making it easier to solve for the equations of motion. This is because it takes into account the inertia of the system, reducing the number of variables needed in the equations.

What is the difference between D'Alembert's reduction principle and the principle of virtual work?

While both principles are used to simplify the equations of motion, the principle of virtual work is used to determine the equilibrium of a system, while D'Alembert's reduction principle is used to determine the equations of motion. Additionally, the principle of virtual work considers external forces, while D'Alembert's reduction principle considers both external and inertial forces.

How is D'Alembert's reduction principle used in real-life applications?

D'Alembert's reduction principle is used in various fields, such as aerospace engineering, robotics, and biomechanics, to model the motion and behavior of complex systems. It is particularly useful in analyzing systems with moving parts or multiple degrees of freedom.

Are there any limitations to D'Alembert's reduction principle?

While D'Alembert's reduction principle is a powerful tool, it does have some limitations. It assumes that the system is in equilibrium and that the equations of motion are linear. It also does not consider friction or other non-conservative forces, which may affect the motion of a system in real-life scenarios.

Similar threads

A Classification of reductive groups via root datum
    • Linear and Abstract Algebra
Replies
3
Views
769
When do these two moving particles come together?
    • Introductory Physics Homework Help
Replies
7
Views
796
On constraint forces and d'Alembert's Principle
    • Classical Physics
Replies
1
Views
2K
Simple Harmonic Oscillator with Boundary Conditions
    • Introductory Physics Homework Help
Replies
10
Views
2K
Help me learn to sketch phase portraits
    • Differential Equations
Replies
2
Views
3K
Conservation of energy: Crane raising a mass
    • Introductory Physics Homework Help
Replies
17
Views
3K
Using D'Alembert's Principle to Find the Fundamental System of an ODE System
    • Calculus and Beyond Homework Help
Replies
1
Views
2K
How Can D'Alembert's Principle Help Solve This Problem?
    • Introductory Physics Homework Help
Replies
6
Views
2K
Plot graph of 1D wave equation (using d'Alembert's formula)
    • Introductory Physics Homework Help
Replies
9
Views
2K
D'Alembert's Principle:- A Falling Box
    • Introductory Physics Homework Help
Replies
1
Views
4K

Hot Threads

Recent Insights

Back
Top