For questions involving the Lagrangian formulation of a dynamical system. Namely, the application of an action principle to a suitably chosen Lagrangian or Lagrangian Density in order to obtain the equations of motion of the system.

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137 views

Can't understand the principle of least action [closed]

I tried many hours to understand the principle of least action, and those hours become days... and I still didn't understand that principle/ and how it relates to Newtonian mechanics? Could someone ...
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1answer
309 views

Canonical momentum Velocity dependent Lagrangian

I have a homework problem wich I think I'm on the verge of solving but need help with some relations: Show that if the potential $U$ in the Lagrangian contains velocity-dependent terms, the ...
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2answers
258 views

A small oscillations of a rod on the cylinder

Let's have the next case. A rod (with mass $m$, length $L$ and a momentum of inertia $I$) at the initial time is located on a cylinder (with radius $R$) surface so that it's (rod's) center of mass ...
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1answer
74 views

Strong interaction and the Lagrangian for electromagnetic interaction

The Lagrangian for electromagnetic field has the following expression: $$ L = -\frac{1}{c^{2}}A_{\alpha}j^{\alpha} - \frac{1}{8 \pi c}(\partial_{\alpha} A_{\beta})(\partial^{\alpha}A^{\beta}) $$ (I ...
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1answer
372 views

Generalized momentum conjugate and potential $U(q, \dot q)$

On Goldstein's "Classical Mechanics" (first ed.), I have read that if $q_j$ is a cyclic coordinate, its generalized momentum conjugate $p_j$ is costant. He obtained that starting from Lagrange's ...
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32 views

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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38 views

Mixed two-point vertex in QFT

I am considering a theory with two fields, say $\phi$ and $\psi$. The Lagrangian contains quadratic terms, i.e., propagators for both fields and a quartic interaction term for one of the fields. ...
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0answers
40 views

Treating $\psi$ and $\psi^{*}$ as independent variables when varying the action [duplicate]

Consider the following Lagrangian (deinsity): $${\mathcal{L}} = \partial_{\mu}\psi^{*} \partial^{\mu}\psi - V(|\psi|^2) $$ In my notes it says that " it's easier (and equivalent) to treat $\psi$ and ...
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30 views

Conditions for hyperregularity

(Definitions from Marsden & Ratiu, ``Introduction to Mechanics and Symmetry''): A Lagrangian is regular if the Hessian $\partial^2 L/(\partial \dot{q}^i \partial \dot{q}^j)$ is weakly non ...
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39 views

How can we describe the trajectory of an object projected into a viscous fluid?

Can we quantitatively describe the motion of a particle inside a fluid? Let us consider the case when an object (say a sphere, so that stoke's law holds true) is projected into a fluid of viscosity ...
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38 views

Another Power Counting/ mass dimension question

Are the mass dimension of the Dirac field different from those of the Klein-Gordon field, or is this just another issue of "cannonical normalization?" For instance if $\mathcal{L}_{KG}=\int ...
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72 views

Center of mass coordinates in Lagrangians and Laplacians

Is there a quick nice and easy way to write Lagrangian's and the classical/quantum Laplacian operator in terms of center of mass coordinates? The algebra is so involved and it has me confused about ...
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0answers
45 views

Lagrangian Field Entropy?

Has anyone investigated the inclusion of a field's entropy in its Lagrangian? I read from information theory that the entropy $H$ of a scalar field $\phi$ distrusted across space is defined as ...
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2answers
145 views

Derivation of Lagrangian?

I know that the Lagrangian $L$ is defined to be $T-V$, i.e. the difference between kinetic energy and potential energy. Also the Action $S$ is defined to be $\int Ldx$ and from this we can derive ...
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0answers
105 views

Why friction force is force of constraint?

My understanding about constraint force is that it is a force which limits the geometry of particle's motion. For example, situations such as the particle trapped in a track or limited in domain can ...
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0answers
121 views

Finding moment of inertia from Lagrange equation

I'm getting the following information: Consider a system consisting of two rotating bars of length $\ell$ and with uniform mass density and each with total mass $m$. The bars are attached to a common ...
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0answers
48 views

Lepton number conservation and global phase transformation

Why the lepton number conservation is connected with the invariance of the lagrangian under global phase (U(1)) transformation of the wave function? How to distinguish global gauge phase and global ...
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1answer
119 views

Block on cart, equation of motion

Consider a rigid block of $b \times h$ having mass $m$ on cart (as depicted below). The cart is given an acceleration $a$, this leads to overturning of the block. The angle of rotation is indicated by ...
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0answers
75 views

Spring Force in a Dynamic Equation

I am working on dynamic simulation of a bipedal robot, I have dynamic equations of a preliminary structure. But Now I have to add some springs to the dynamics. I am having a problem of how to account ...
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0answers
26 views

Expansion of $L(v^2 + 2\vec{v}\cdot\vec{\epsilon}+\epsilon^2)$ [duplicate]

How can I find the expansion of the Lagragian (it it only dependent on $v^2$) $L(v^2 + 2\vec{v}\cdot\vec{\epsilon}+\epsilon^2)$ in powers of $\vec{\epsilon}$ ? (From L.Landau, E. Lifshitz, Mechanics , ...
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0answers
39 views

The definition of Lagrangian [duplicate]

I have learned Lagrange's equation, and we have Lagrangian defined as $$L=T-V$$ My question is why Lagrangian is defined like this rather than other format such as $T+V$ or something else.
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0answers
49 views

What is the “momentum” referred to in the energy-momentum tensor

What is the "momentum" referred to in the energy momentum tensor from GR? Is it $m\dot{x}$ or is it the canonical momentum $\frac{d}{dt} \left(\frac{\partial L}{\partial \dot{x}}\right)$ Also, I ...
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2answers
256 views

Math required for learning Lagrangian mechanics [duplicate]

How much knowledge of maths is required for learning Lagrangian mechanics? Also from where can I learn this math?
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0answers
37 views

How can a transversality condition be invoked to reduce the Euler-Lagrange equation?

I asked this question regarding the Euler-Lagrange equation at MSE and have gotten no response. I will ask it here too. I think I might have more luck here since the E-L equation is at the core of ...
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0answers
37 views

Lagrangian - Particle wave interaction

Assume that we got a Lagrangian of a classical wave $\phi(x,t)$ and a classical particle $q(t)$. The interaction term in the lagrangian is $$ L_{int}=\frac g 2 \dot{\phi}(x=q(t),t)$$ It is very ...
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421 views

Scalar field lagrangian in curved spacetime

I am studying inflation theory for a scalar field $\phi$ in curved spacetime. I want to obtain Euler-Lagrange equations for the action: $$ I\left[\phi\right] = \int ...
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1answer
54 views

Doubt about coordinates and point of equilibrium

I'm solving an exercise about small oscillations and I have a doubt about coordinates that I have to use. This is the text of the exercise: "A bar has mass M and lenght l. Its extremity A is hooked ...
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1answer
189 views

A Type of Pendulum [closed]

Is there any chance that $$rtl(\ddot\omega+\ddot\phi)\cdot\sin{(\phi+\omega t)}- gl\dot\phi \cdot \sin{\phi} + ltr\dot\omega(\dot\phi^2-\dot\omega)\cdot \cos{(\phi+\omega t)}-gtr\cos{(\omega ...
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0answers
331 views

How to find angular velocity of a point inner a circumference

Let's consider a cicumference that have the center in the origin of axes and rotates around x-axes. Let's stick a bar in a point $A$ of this circumference and at the end of the bar let's stick a mass ...
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0answers
160 views

Describing the movement of the object in a particular situation in Lagrangian way

Suppose there is a object M, (sliding motion) moving by the initial speed $v$ and the initial location $x_0$. Otherwise noted, friction is assumed to be nonexistent. It then meets a circular mold ...
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0answers
183 views

Comparing Lagrangian in Special Relativity vs General Relativity for a weak gravitational field

This is a sequel to this question. Who knows a difference between the Lagrangian in SR and GR for a weak gravitational field in non-relativistic case? What is the reason of this difference?
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1answer
205 views

Scalar field lagrangian and potential

This question is a continuation of this Phys.SE post. Scalar field theory does not have gauge symmetry, and in particular, $\phi\to\phi−1$ is not a gauge transformation. but why? and I want see the ...
-1
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1answer
243 views

Lagrangian formulation for relativistic quantum fields

The Lagrangian for a real scalar field is: $$\mathcal{L}=\frac{1}{2}\eta^{\mu \nu}\partial_{\mu}\phi\partial_{\nu}\phi-\frac{1}{2}m^2\phi^2 $$ How can I derive the dynamics of this field from this ...
-1
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1answer
142 views

Linear/ non linear Scalar field theory

How do I understand that the action for the free relativistic scalar field theory is non linear? What will be the associated interaction potential of that equation?
-1
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1answer
161 views

Quantum tunneling in Field theory with Time dependent potential

What should be the limits of integration for euclidean action $S(\phi)$ in 3d and 4d? This action is negatively exponentiated to calculate the decay rate. I suspect that it is variable limit problem. ...
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1answer
206 views

Classical Mechanics - Equation of motion, Lagrangian, Newtons 2nd Law [closed]

I really don't even know where to start with this question any help would go very very far. http://imgur.com/g4KxNY5