Linked Questions

4
votes
2answers
888 views

Why is potential energy defined for only a conservative force? [duplicate]

I want direct answer for this and some interpretation with example. why do we need conservative force to define potential energy? what is wrong with non-conservative force and other? I have seen many ...
-4
votes
1answer
52 views

Work Power Energy [duplicate]

Why is work done by non-conservative force path dependent? If friction does work then it is given by Force * displacement (no matter what path i take).
0
votes
1answer
40 views

Definition of non-conservative force [duplicate]

In defining conservative force, we say that "The potential energy difference is path independent." However, as far as I understand, potential energy only exists when there is a force field. ...
1
vote
0answers
15 views

Are the gradient field are the only fields which are only conservative? [duplicate]

I have found that gradient fields are always conservative. But for my knowledge I wanna ask "are the gradient fields are only fields which are conservative"? I mean is it necessary that a field which ...
65
votes
14answers
8k views

Lagrangians not of the form $T-U$

My Physics teacher was reluctant to define Lagrangian as Kinetic Energy minus Potential Energy because he said that there were cases where a system's Lagrangian did not take this form. Are you are ...
15
votes
4answers
2k views

What exactly makes a force conservative?

I get that forces can be classified as either conservative or non-conservative, depending on whether the work done in a round trip is zero or non-zero. What property of the force makes it to be, ...
16
votes
4answers
3k views

Why can't we ascribe a (possibly velocity dependent) potential to a dissipative force?

Sorry if this is a silly question but I cant get my head around it.
10
votes
1answer
3k views

How do non-conservative forces affect Lagrange equations?

If we have a system and we know all the degrees of freedom, we can find the Lagrangian of the dynamical system. What happens if we apply some non-conservative forces in the system? I mean how to deal ...
14
votes
3answers
767 views

Motivation for Potentials

This is a hypothetical question about "pedagogy". Let's say I am trying to take someone who has just a very small amount of knowledge about Newtonian mechanics and convince them that the Lagrangian ...
0
votes
3answers
4k views

Why can't we define a potential energy for a non-conservative force? [closed]

We could define potential energies for non-conservative forces too and then we could conserve it with kinetic and potential energy as we know it. But no one does that. Why is this? Please explain. Any ...
10
votes
2answers
4k views

Can a force in an explicitly time dependent classical system be conservative?

If I consider equations of motion derived from the principle of least action for an explicitly time dependent Lagrangian $$\delta S[L[q(\text{t}),q'(\text{t}),{\bf t}]]=0,$$ under what ...
8
votes
2answers
417 views

A false proof of drag force being conservative

Consider a particle moving along some trajectory in the $x$-$y$ plane, in a viscous medium. Then its equation of motion is given by: $$\mathbf{F}_d = - b \mathbf{v} .$$ it's well-known from the ...
5
votes
2answers
364 views

Does d'Alembert principle hold for non-conservative forces?

I know that D'Alembert's principle doesn't hold for sliding friction. But does it hold for any non-conservative force (other than sliding friction) or not? Could you give some examples of non-...
2
votes
3answers
1k views

Understanding the math behind velocity-dependent conservative forces, Part 1

In a notable answer to this question, Qmechanic formulates conditions for "conservative" velocity-dependent forces (e.g. the Lorentz force, but not velocity-proportional friction) that are analogous ...
3
votes
2answers
693 views

Generalized definitions of Lagrangian and Hamiltonian functions

When we enter into the scope of Analytical mechanics we usually start with these two primary notions: Lagrangian function & Hamiltonian function And usually textbooks define Lagrangian as $L=T-V$ ...

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