Linked Questions
65 questions linked to/from How do I show that there exists variational/action principle for a given classical system?
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Is the Lagrangian formulation a mathematical inevitability? [duplicate]
An analogy with functions:
Say, we have a function $f(x)$ and we have an equation to solve, $f(x)=0$. We can always re-formulate the problem of solving $f(x)=0$ with the problem of extremising $F(x)$, ...
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Is there any reason for principle of least action to be true? [duplicate]
My question is not rigidly related to physics. The principle of least actions says that for any dynamical system there exists a function parameterized by $q$'s and $\dot{q}$'s such that the line ...
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Is action principle trivial? [duplicate]
Given a function $f(t)$, is it possible to construct Lagrangian $\mathcal{L}$ such that
$\frac{\mathrm{d}}{\mathrm{d}t}\frac{\partial\mathcal{L}}{\partial \dot{f}}=\frac{\partial\mathcal{L}}{\partial ...
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Why does it seem like there is always a Lagrangian? [duplicate]
All the fundamental laws of physics can be written in terms of an action principle. This includes electromagnetism, general relativity, the standard model of particle physics, and attempts to go ...
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Action principles and covariant equations [duplicate]
Can every physically sound differential equation, that is covariant, deterministic etc. be derived by extremising a suitable action using a suitable lagrangian, that may be arbitary. Is this a ...
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Why should physical theories always have a Lagrangian formalism? [duplicate]
I've often heard that every physical theory has some kind of Lagrangian formalism, or a formalism in terms of a principle of stationary action. The Standard Model has one, General Relativity has one, ...
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What systems can the Principle of Least Action be applied? [duplicate]
When reading about the Calculus of Variation and Hamilton's principle I come across quotes like this
Hamilton's principle states that the differential equations of motion for any physical system ...
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Given equations of motion, how can we check if there is a lagrangian from which we can derive them? [duplicate]
Suppose we are given a set of equations of motion for $N$ bodies, which generically will go like this
\begin{equation}
\frac{d^2\mathbf{r}_i}{dt^2}=\mathbf{F}_i \left((\mathbf{r}_i)_{1 \leq i \leq N},...
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Is there a method to obtain a Lagrangian from the equations of motion? [duplicate]
From the standpoint of the mathematical framework behind Lagrangians and their corresponding action, is there a method to invert the process?
If not, is this an open question or is there some aspect ...
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Can the Euler-Lagrange equation be used to derive the stationary action formula? [duplicate]
From what I understand I can use the Euler-Lagrange equation to find the function ( Let us call L. ) where L can be the function as stated in the action formula.
But how difficult is it to actually ...
user86411
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Fields that lend themselves to variational principles? [duplicate]
In physics, we often describe the dynamic properties of fields using variational principles like defining an action or a Lagrangian. A field however is simply some function of space $\phi(x)$ so I ...
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Must there exist a Lagrangian for any 2nd order ordinary derivative equation? [duplicate]
We know if there exist a Lagrangian of some ODE, then it must exist many equivalent Lagrangian.
My question:
Then must there exist a Lagrangian for any 2nd order ODE? If not, do we have some ...
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Can Lagrangians model all possible dynamics? [duplicate]
We use Lagrangians and variational calculus for almost all of physics, from Newtonian mechanics to QFT.
Is there any theorem in mathematics that guarantees that all possible dynamics of objects (say ...
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Is It Possible to Express all fundamental forces in the form of generalized potentials? [duplicate]
I have Started reading Hamilton's Principle or Principle of Least Action In first course of Undergraduate classical mechanics.
So, I think it becomes easier to apply the Variational principles if ...
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Can we go from equations of motion back to Lagrangian? [duplicate]
We always go in one direction, from Lagrangian to equations of motion (classical mechanics). But is it possible to go the opposite way, from equation of motion to Lagrangian? Suppose we have an ...
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