# Questions tagged [equations-of-motion]

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### Why can we use the equation of motion to calculate the amplitude in “Quantum Field Theory”?

I am reading the chapter on electron-proton scattering from "Quantum Field Theory in a Nutshell". The author calculates the amplitude of the electron-proton scattering (up to the second order). The ...
3answers
187 views

### In what sense are the equations of motion conserved by symmetries?

I am studying variational principles and I have been reading this set of notes by Townsend. In the first paragraph of Section 9, Townsend defines what it means for a transformation to be a symmetry of ...
1answer
104 views

### Rotation as an example of symmetry in classical mechanics

I modified the question because it was confused. On my book there is this mathematical definition of symmetry transformation: "The equations of motion have a symmetry, if the solutions of the ...
1answer
30 views

### Can we ignore the scalar field (dilaton) term in the Polyakov sigma-model action when deriving the classical equations of motion?

I have the full Polyakov sigma model action: \begin{equation} \begin{split} &S=S_P + S_B + S_\Phi = \\ &- {1 \over 4 \pi \alpha'} \Big[ \int_\Sigma d^2\sigma \sqrt{-g} g^{ab} \partial_a X^\mu ...
3answers
315 views

### Why intuitively, do we define symmetries as transformations that map solutions of the equations of motion into other solutions?

Of course, strictly speaking, a symmetry is always a transformation that leaves a given object unchanged. But I'm curious why observable symmetries of physical systems are exactly those ...
1answer
36 views

### Does the equation of ball going up in gravity straight up with a vertical initial velocity hold when it's coming down?

Suppose a ball is thrown up and having the same altitude at different times. So should the equation of motion $v_0t - gt^2$ which I derive from balancing forces hold for both the times when the ball ...
0answers
208 views

### Upward Moving Cable Car [closed]

A $1500$ kg cable car moves vertically by means of a cable that connects the ground and the top of the hill. What is the tension in the supporting (massless) cable when the cab, originally moving ...
2answers
125 views

### Can an Equation of Motion Do More?

My usual expectation is that an equation of motion should give me the time-evolution of a system given an initial condition. But I am curious as to can an equation of motion do more than that? In ...
3answers
120 views

### Are symmetries in the equation necessarily symmetries in the corresponding solution(s)?

I wonder whether the symmetries in the equations (such as the heat equation, the wave equation, the Schrödinger equation, Maxwell equations) are reflected into their solution(s). I.e., assuming that ...
1answer
187 views

### Equations of motion of a cylinder on a horizontal plane

How would I go about deriving the equations of motion for the motion of the centre of mass of the cylinder in this system: The cylinder has mass $M$ and radius $R$ and the small mass $m$ is being ...
1answer
465 views

### Transformation of generalized coordinates

One of the advantages of Lagrangian formulation is that the equations of motion have the same form regardless of the choice of generalized coordinates. Suppose that a system has $s$ degrees of freedom,...
3answers
133 views

### Do the equations of motion have specific characteristics?

I solved a classical mechanics problem in a form somewhat like this: $$x(t)=t^2+5t$$ $$y(t)=t^3$$ $$z(t)=5.$$ The problem asked me to find the equations of motion of an object. From my ...
2answers
377 views

### Question about Type IIB supergravity equations of motion

This is probably a dumb question, but I'm a mathematician who's been trying to understand the equations of motion for Type IIB supergravity, and I'm not quite sure I understand what's going on with ...
1answer
94 views

### What does it mean to find an equation of motion, given vector functions that describe both the object's position and velocity?

I don't really understand how to approach a problem that asks to find the equation of motion. Intuitively, I would guess that an "equation of motion" is an equation where the particle's position is ...
2answers
203 views

### Showing the invariance of the equations of motion

It is strange to me that for a symmetry which involves $\dot{x}$, there seems to always appear a term with $\dddot{x}$ in the variation of the equations of motion, which doesn't makes much sense. I ...
3answers
214 views

### Is it valid to replace the equations of motion inside a symmetry?

For example, this symmetry: $$\delta q^{i}=\epsilon(q^{i}-2\dot{q}^{i}t)$$ it's derivative is: $$\delta\dot{q}^{i}=-\epsilon(\dot{q}^i +2\ddot{q}^i t)$$ There appears $\ddot{q}^{i}$ in this ...
1answer
202 views

### Is it strictly necessary to require gauge invariance of the action and equations of motion?

When writing down an action for a gauge theory, we require that the action be gauge invariant. This is typically taken to mean that the action must be written explicitly in terms of gauge invariant ...
1answer
88 views