Linked Questions

3 votes
1 answer
2k views

Lagrangian formalism and dissipative systems [duplicate]

Why the central concepts of classical mechanics, viz. Lagrangian and Hamiltonian formalisms cannot address constraint forces like friction and others in dissipative systems?
k.kulkarni19952's user avatar
0 votes
1 answer
92 views

If a force depends on velocity, then why is the force not conservative? I need a formal proof [duplicate]

I am currently an undergraduate taking a course on Newtonian mechanics. The lecturer defines a force to be conservative if there exists a scalar function (we call it potential function), say $V(x,y,z)$...
IncredibleSimon's user avatar
86 votes
15 answers
15k views

What are examples of Lagrangians that 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 ...
ZAC's user avatar
  • 1,307
41 votes
7 answers
11k views

Is there a proof from the first principle that the Lagrangian $L = T - V$?

Is there a proof from the first principle that for the Lagrangian $L$, $$L = T\text{(kinetic energy)} - V\text{(potential energy)}$$ in classical mechanics? Assume that Cartesian coordinates are used. ...
Chin Yeh's user avatar
  • 761
35 votes
2 answers
10k views

Lagrangian and Hamiltonian EOM with dissipative force

I am trying to write the Lagrangian and Hamiltonian for the forced Harmonic oscillator before quantizing it to get to the quantum picture. For EOM $$m\ddot{q}+\beta\dot{q}+kq=f(t),$$ I write the ...
user avatar
20 votes
2 answers
7k views

What causes a force field to be "non-conservative?"

A conservative force field is one in which all that matters is that a particle goes from point A to point B. The time (or otherwise) path involved makes no difference. Most force fields in physics ...
Tom Au's user avatar
  • 313
12 votes
2 answers
19k views

Euler-Lagrange equations and friction forces

We can derive Lagrange equations supposing that the virtual work of a system is zero. $$\delta W=\sum_i (\mathbf{F}_i-\dot {\mathbf{p}_i})\delta \mathbf{r}_i=\sum_i (\mathbf{F}^{(a)}_i+\mathbf{f}_i-\...
jinawee's user avatar
  • 12.5k
18 votes
4 answers
3k views

D'Alembert's Principle: Necessity of virtual displacements

Why is the d'Alembert's Principle $$\sum_{i} ( {F}_{i} - m_i \bf{a}_i )\cdot \delta \bf r_i = 0$$ stated in terms of "virtual" displacements instead of actual displacements? Why is it so necessary ...
Sandesh Kalantre's user avatar
7 votes
3 answers
2k views

Higher order derivatives - Equation of motion

One possible starting point to create a physical theory is the Lagrangian $L$. There we assume that the variation of the action $\delta S = \delta \int_{-\infty}^\infty dt \ L = 0$. In classical ...
physicsGuy's user avatar
  • 1,034
8 votes
2 answers
1k views

Why can't conservative forces depend on velocity?

In my mechanics lecture notes, it is written that, for a force $F$, To be conservative, $F$ must be a function of position only: forces that depend on velocity, time, etc. cannot be conservative. ...
sam wolfe's user avatar
  • 189
5 votes
3 answers
4k views

Conservation of Energy and Momentum Regarding Forces - clarification needed

The other day, my teacher stated something along the lines of, "Conservation of momentum is not violated by the actions of internal forces, but the conservation of energy is violated. Energy is ...
Joe's user avatar
  • 886
4 votes
4 answers
3k views

What is a non-conservative system?

I've been searching a bit on the internet for a mathematical description of a non-conservative system, but I could not find it. I'm looking for a good description. Wikipedia does not have an article ...
Natural Number Guy's user avatar
10 votes
2 answers
515 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 ...
Omar Nagib's user avatar
  • 3,093
3 votes
4 answers
3k views

How do I include friction due to normal force in Lagrange Equations?

I am going through the Goldstein book on classical mechanics and the after he derived the Lagrange equations he used Rayleigh dissipation function to include friction as a generalized force. In school ...
QuantumEmbryo's user avatar
2 votes
2 answers
3k views

Is the potential term in a Lagrangian velocity-dependent?

I know that the Lagrangian of a system has to be dependent on the coordinate (as the type of potential in it is dependent on the coordinate) and on velocity and time (per KE and PE, respectively). ...
user575201's user avatar

15 30 50 per page