Transforming Lagrangian without changing the equations of motion.

AI Thread Summary
Transforming a Lagrangian without altering the equations of motion can be achieved by adding a total time derivative or multiplying the Lagrangian by a constant. However, there are broader possibilities through canonical transformations, which include modifications defined by the modified Hamilton's principle. The principle states that the difference between the original and transformed variables can include a total time derivative. The discussion raises questions about additional transformations that can be applied to the Lagrangian without changing variables. Overall, the exploration of canonical transformations and their implications for Lagrangian mechanics remains a complex topic.
alemsalem
Messages
173
Reaction score
5
I know that it works with adding a total time derivative and multiplying the Lagrangian by a constant.
are these the only things that can be done to a Lagrangian such that the equations of motion have the same solutions q(t).

Thanks!
 
Physics news on Phys.org
There is a wider class of so called canonical transformations.
 
Dickfore said:
There is a wider class of so called canonical transformations.

These are the ones I'm having a problem with. the modified Hamilton's principle gives this definition for a canonical transformation:
pq - H = PQ - K + (total time derivative).. and that's because you can add a total time derivative inside the integral for the action.
I also want to know if there is more transformations on the Lagrangian without a change of variables.

Thanks :)
 

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 'Average velocity as a weighted mean'

Hello everyone, Consider the problem in which a car is told to travel at 30 km/h for L kilometers and then at 60 km/h for another L kilometers. Next, you are asked to determine the average speed. My question is: although we know that the average speed in this case is the harmonic mean of the two speeds, is it also possible to state that the average speed over this 2L-kilometer stretch can be obtained as a weighted average of the two speeds? Best regards, DaTario
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 »

Similar threads

A Equations of Motion for Torsional Inverted Pendulum on a moving cart
Replies
2
Views
1K
I Using reference frames for derivation of Lagrangian
Replies
25
Views
2K
I Types of symmetries in Lagrangian mechanics
Replies
3
Views
2K
I Adding total time derivative to Lagrangian/Canonical Transformations
Replies
2
Views
192
The Lagrange equations from mechanics
Replies
5
Views
1K
I Metal Ball Rolling in a Parabolic Bowl in the presence of a magnet
Replies
1
Views
1K
A Find Euler-Lagrange Equations w/Given Init Pos & Vel
Replies
12
Views
2K
I Why are there 2s -1 independent integrals of motion?
Replies
4
Views
2K
I Noether’s theorem -- Question about symmetry coordinate transformation
Replies
4
Views
1K
I Calculus Question within Lagrangian mechanics
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top