A Can Newton's Method Solve Freer Motion?

  • A
  • Thread starter Thread starter Juli
  • Start date Start date
  • Tags Tags
    Lagrange Newton
AI Thread Summary
Newton's method can be used to solve equations of motion even in cases of free motion, contrary to the assumption that Lagrangian mechanics is necessary. Lagrange formulations, whether with constraints or generalized coordinates, are applicable to unconstrained systems and may simplify the derivation of constants of motion. The main challenge arises when dissipative forces, such as friction, are present, which complicates the equations of motion. The discussion clarifies that the ability to solve these equations is not inherently tied to the choice of theoretical framework. Ultimately, both Newton's and Lagrangian methods have their merits depending on the specific conditions of the motion being analyzed.
Juli
Messages
24
Reaction score
6
Hello everyone,

my question is, if there is a case, where you can't you Langrange (1 or 2) but only Newton to solve the equation of motion?
My guess is, that it might be, when we have no restrictions at all, so a totally free motion.
Does anybody know?
 
Physics news on Phys.org
What do you mean by Lagrange 1 and 2? That does not seem like standard nomenclature to me. Please be specific.

Generally, the equations of motion are differential equations and whether they can be solved or not does not depend on the theory you used to derive them. Where you could fail is in arriving at a set of equations of motion.
 
Last edited:
Usually "Lagrange 1" is the formulation with the (holonomic) constraints treated with Lagrange multipliers, while "Lagrange 2" is the formulation in terms of an appropriate set of "generalized coordinates".
 
Regardless, it should probably be pointed out that Lagrange mechanics is perfectly applicable to systems without constraints. It could even be argued it does better in ease of deriving constants of motion etc. Where you can run into issues is when there are dissipative forces (eg, friction) acting on the system.
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
View full post »

Thread 'Inclined treadmills and Galilean Invariance'

This has been discussed many times on PF, and will likely come up again, so the video might come handy. Previous threads: https://www.physicsforums.com/threads/is-a-treadmill-incline-just-a-marketing-gimmick.937725/ https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/ https://www.physicsforums.com/threads/how-do-we-calculate-the-energy-we-used-to-do-something.1052162/
View full post »

Similar threads

I Using reference frames for derivation of Lagrangian
Replies
25
Views
2K
A Equations of Motion for Torsional Inverted Pendulum on a moving cart
Replies
2
Views
1K
B What is the Absolute Value of the Normal force on a block on this wedge?
Replies
3
Views
1K
I Why is it Impossible to Solve the Three Body Problem Analytically?
Replies
6
Views
4K
Learning DEs: Solving 2nd Order Differential Equations
Replies
1
Views
901
Why were Newton's laws of motion discovered so late?
2
Replies
66
Views
9K
Equations of motion of damped oscillations due to kinetic friction
Replies
6
Views
1K
Can analytical mechanics be deduced from Newtonian mechanics?
Replies
22
Views
2K
I Acceleration in Newton's second law
Replies
5
Views
2K
I Can Any Quantifiable Variable Serve as a Coordinate in Euler-Lagrange Equations?
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top