Linked Questions
36 questions linked to/from Why can't we ascribe a (possibly velocity dependent) potential to a dissipative force?
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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?
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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 $V(x,y,z)$...
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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 ...
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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. ...
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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 ...
user56199
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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 ...
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Euler-Lagrange equations and friction forces
We can derive Lagrange equations supposing that the virtual work of a system is zero.
$$\delta W=\sum_i (\mathbf{F}_i-\dot {\mathbf{p}_i})\delta \mathbf{r}_i=\sum_i (\mathbf{F}^{(a)}_i+\mathbf{f}_i-\...
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D'Alembert's Principle: Necessity of virtual displacements
Why is the d'Alembert's Principle
$$\sum_{i} ( {F}_{i} - m_i \bf{a}_i )\cdot \delta \bf r_i = 0$$
stated in terms of "virtual" displacements instead of actual displacements?
Why is it so necessary ...
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Higher order derivatives - Equation of motion
One possible starting point to create a physical theory is the Lagrangian $L$. There we assume that the variation of the action $\delta S = \delta \int_{-\infty}^\infty dt \ L = 0$.
In classical ...
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Why can't conservative forces depend on velocity?
In my mechanics lecture notes, it is written that, for a force $F$,
To be conservative, $F$ must be a function of position only: forces that depend on velocity, time, etc. cannot be conservative.
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Conservation of Energy and Momentum Regarding Forces - clarification needed
The other day, my teacher stated something along the lines of, "Conservation of momentum is not violated by the actions of internal forces, but the conservation of energy is violated. Energy is ...
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What is a non-conservative system?
I've been searching a bit on the internet for a mathematical description of a non-conservative system, but I could not find it. I'm looking for a good description.
Wikipedia does not have an article ...
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A false proof of drag force being conservative
Consider a particle moving along some trajectory in the $x$-$y$ plane, in a viscous medium.
Then its equation of motion is given by:
$$\mathbf{F}_d = - b \mathbf{v} .$$
it's well-known from the ...
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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 ...
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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). ...
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