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 '1:1 versus 2:1 Mechanical Advantage debate'

The rope is tied into the person (the load of 200 pounds) and the rope goes up from the person to a fixed pulley and back down to his hands. He hauls the rope to suspend himself in the air. What is the mechanical advantage of the system? The person will indeed only have to lift half of his body weight (roughly 100 pounds) because he now lessened the load by that same amount. This APPEARS to be a 2:1 because he can hold himself with half the force, but my question is: is that mechanical...
View full post »

Thread 'Newton's first law?'

Some physics textbook writer told me that Newton's first law applies only on bodies that feel no interactions at all. He said that if a body is on rest or moves in constant velocity, there is no external force acting on it. But I have heard another form of the law that says the net force acting on a body must be zero. This means there is interactions involved after all. So which one is correct?
View full post »
Thread 'Beam on an inclined plane'

Thread 'Beam on an inclined plane'

Hello! I have a question regarding a beam on an inclined plane. I was considering a beam resting on two supports attached to an inclined plane. I was almost sure that the lower support must be more loaded. My imagination about this problem is shown in the picture below. Here is how I wrote the condition of equilibrium forces: $$ \begin{cases} F_{g\parallel}=F_{t1}+F_{t2}, \\ F_{g\perp}=F_{r1}+F_{r2} \end{cases}. $$ On the other hand...
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
895
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