Tagged Questions

A set of numbers used to quantify location in space.

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Prove that the spacetime interval is not invariant under Galilean transformations [closed]

The spacetime interval $(\Delta s)^2 = (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 - c^2(\Delta t)^2$ is invariant under the Lorentz transformation and this isn't the case for the Galilean ...
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Evaluating derivatives with respect to certain vector axis

So, I am trying to work in Spherical coordinates. I have a predefined fixed axis, $\hat{v}_0$, so that $\alpha=\vec{r}.\hat{v}_0$ Now, I am interested in the following: f(r,\alpha)=\...
0answers
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Accelerometer Pitch and Roll Calculation

I am developing an application for a device that needs to know its tilt/orientation, specifically, pitch and roll. Roll is positive if the right side of the device is elevated, and pitch is positive ...
1answer
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Ergosphere in different coordinates

I am currently working with the concept of an ergosphere and I was wondering if it has any meaning to consider the ergosphere after changing coordinates. I mean if someone looks only on the sign of g_{...
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1answer
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Confusing concepts in proof of spherical addition theorem

In http://scipp.ucsc.edu/~haber/ph116C/SphericalHarmonics_12.pdf, section 4, pages 6..9 is a proof of the spherical harmonics addition theorem. Page 8 has eq.(25), an application of Laplace series: ...
2answers
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Why does the Lorentz transformation have to be a linear transformation? [duplicate]

In my textbook, they say the following statements before doing a proof for the Lorentz transformation: We know that the Galilean transformation $x' = x - vt$ is incorrect, but what is the ...
1answer
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Why does a system have to be holonomic?

So I'm doing some work from Taylor's mechanics book. He says for the problems in the book, we require the system to be holonomic - that is the number of generalized coordinates = number of Deg. of ...
1answer
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Eulerian angle understanding

I have alot of confusion with Eulerian angle so first of all I would like to address something I don't understand from the book and maybe that would shed some light on the intuition of eulerian angles....
2answers
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What coordinate systems allows the magnitude of the basis vectors to change with position?

I'm familiar with coordinate systems where the direction of the basis vectors changes with position, but I haven't come across any where the relative magnitude of the basis vectors themselves are ...
0answers
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Is Lorentz Transformation about the difference of coordinates or coordinates of itself?

I have seen different authorities talking about different interpretation of Lorentz transformation. In his book 'Introduction to Classical Mechanics', David Morin states We always talk about eh ...
1answer
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Non-inertial frames in Lagrangian mechanics?

Building on this Phys.SE post I am interested in how non-inertial frames can be considered in Lagrangian mechanics. My understanding is that changing the reference frame causes a transformation of the ...
1answer
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Transform velocities from one frame to an other within a rigid body

I come from non-physics background but just came to face the following problem. I have a rigid body with two attached frames of reference A and A'. I know: the rotation and translation between A ...
1answer
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Co-ordinate rotations

I need help transforming a magnetic field vector from one co-ordinate system to another. I have the components of the Earth's magnetic field in a co-ordinate system with z facing radially into the ...
1answer
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Free-fall path into a black hole in Kruskal Coordinates

If an object at t=0 begins to free-fall into a black hole from X in Kruskal coordinates (https://en.wikipedia.org/wiki/Kruskal%E2%80%93Szekeres_coordinates), what does its path on the Kruskal-Szekeres ...
1answer
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Non-inertial system [duplicate]

Supposing I am in a non-inertial system and I don't know what forces are acting. How can I test EXPERIMENTALLY and in practice to be in a non inertial system? If I am in a system and I don't know how ...
4answers
870 views

Why is displacement negative during free fall?

I am confused by this question. Displacement is shortest path travelled by an object, but I had seen in my book that during free fall displacement is negative.
1answer
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$\sqrt{\frac{\omega ^2}{c^2}-k_z^2}$ in cylindrical harmonics

The radial component of the solution of the wave equation in cylindrical coordinates is $$J_\nu \bigg(\rho\sqrt{\frac{\omega ^2}{c^2}-k_z^2}\,\,\bigg).$$ But I always thought that $\frac \omega c$ ...
0answers
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Coordinate Transformation across different media

I have an arrangement that is as follows : (1) inner cylinder(radius r1) filled with water (2) outer cylinder(concentric, radius r2>r1) made of glass I have a sensor S1 at radius r(r1) at angle beta. ...
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Meaning of Proper time

Sorry for a bit of a basic question, but want to clarify things in my head. Is proper time quantified by the amount of physical process that an object, or physical system undergoes, for example the ...
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Test bodies general relativity

I'm studying section 82 of the Landau & Lifshitz Field Theory vol.2 In this page it's written that the relative position of test bodies can't remain unchanged during time. And ok with this. But ...
1answer
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Invariant equations of motion under Lorentz transformations

My question regards the statement that an equation of motion may be invariant under a Lorentz transformation I just finished watching the Stanford University special relativity lectures on special ...
2answers
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Are spherical coordinates distances or angles?

I've become confused about spherical coordinates when dealing with electric fields. The way I always understood spherical coordinates is something like the below picture. To define a vector, you give ...
2answers
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Best coordinate system for Projectile motion [closed]

What is the best coordinate system for describing the projectile motion? Rectangular coordinate system or n-t(normal and tangential) coordinate system.
1answer
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Manifolds, unit 2-sphere and stereographic projection

I am always passing through this example while reading about manifolds that I don't quite get. It is when describing the unit 2-sphere $S^2$ as an example of a manifold. They say, initially it may ...
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How do I compute the galactic cooridinates of the Earth for a given date?

The question is simple enough, but I wasn't able to find any tools online. Does anyone know of one, or a simple formula?
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Under what representation do the Christoffel symbols transform?

I often read the statement, that the Christoffel symbols aren't tensors. But then, under which representation do they transform?
2answers
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At what point does force stop translating an object and start purely rotating it? [duplicate]

At what point (or distance) from the axis of rotation, does force applied on a rigid body stop translating and purely rotating the body? Can such a point even exist? Does the body always have to ...
1answer
212 views

Description of charged sphere with Heaviside function in cylindrical coordinates

I need to describe density of charge of uniformly charged sphere (radius R, total charge Q, position of centre (0,0,0)) with Dirac delta function and Heaviside step function. The hard part is to ...
1answer
95 views