Linked Questions
49 questions linked to/from Lagrangian and Hamiltonian EOM with dissipative force
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How can dissipative/friction terms be incorporated into a Lagrangian? [duplicate]
I'm trying to find a suitable Lagrangian for a damped harmonic oscillator, a system that satisfies the following equation of motion:
$$m \ddot{x} + \gamma \dot{x} + \frac{d\phi}{dx} = 0.$$
What I ...
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Is it possible to formulate a Hamiltonian for a damped system? [duplicate]
I recently found out that it is possible to formulate a Hamiltonian for a system with time-dependent coordinates such that the Hamiltonian is not the same as the energy When is the Hamiltonian of a ...
3
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1
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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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Friction in Lagrangian Method [duplicate]
A uniform, flexible chain of length $l$, mass $m$, hangs off a frictionless table-top of height greater than $l$. The length of the part of rope hanging off is $x$. Gravity accelerates the part of the ...
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Damped harmonic oscillator Lagrangian $f(t)(\ddot{x}+\alpha\dot{x}+\omega^2x)=0$ determinate a function $f(t)>0$ [duplicate]
I'm considering a damped harmonic oscillator
$$\ddot{x}+\alpha\dot{x}+\omega^2x=0 \,\,\,\,\,\,\,\,\,\,\, \alpha \neq 0$$
I know that this equation could not be a lagrangian equation originated from a ...
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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 the principle of least action a boundary value or initial condition problem?
Here is a question that's been bothering me since I was a sophomore in university, and should have probably asked before graduating:
In analytic (Lagrangian) mechanics, the derivation of the Euler-...
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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.
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4
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How do I show that there exists variational/action principle for a given classical system?
We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's ...
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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 ...
user58143
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Is David Tong incorrect in this remark about classical mechanics in his QM lectures?
In page 11 of his Quantum Mechanics lectures, we have the following quote:
It turns out that not all classical theories can be written using a Hamiltonian. Roughly speaking, only those theories that ...
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Can one write down a Hamiltonian in the absence of a Lagrangian?
How can I define the Hamiltonian independent of the Lagrangian? For instance, let's assume that i have a set of field equations that cannot be integrated to an action. Is there any prescription to ...
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Damped oscillator: time-reversal, time-translation and dissipation
The equation of motion of a damped oscillator $$\frac{d^2x}{dt^2}+\gamma\frac{dx}{dt}+\omega_0^2x=0$$ which is invariant under time-translation $t\rightarrow t+a$, but not under time reversal $t\...
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How do Hamilton's equations deal with non-conservative forces?
I have searched everywhere I know to look but I cannot find out how Hamilton's equations deal with non-conservative forces. In my understanding, Lagrangian mechanics deals with this as follows: the ...
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Paths in phase space can never intersect, but why can't they merge?
Page 272 of No-Nonsense Classical Mechanics sketches why paths in phase space can never intersect:
Problem: It seems to me this reasoning only implies that paths can never "strictly" ...
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