0
votes
2answers
45 views

Projections in Polar coordinate system

I really understand what projections in Cartesian coordinate system, I can imagine this, but I absolutely do not understand projection in polar system. For example, I have a speed, $U$, and I must ...
0
votes
0answers
26 views

A basic relation in spherical coordinates [migrated]

Why is it that $$x\partial_x+y\partial_y+z\partial_z=r\partial_r~?$$ I know that $$r^2=x^2+y^2+z^2,$$ but how is this relation implied?
0
votes
0answers
21 views

How to find a vector normal to a cylinder in cylindric coordinates? [migrated]

I'm trying to solve a problem which demands to multiply a vector M and vector normal to a cylinder's surface in cylindric coordinates. Height of the cylinder is infinite and its radius is R. So how do ...
0
votes
2answers
29 views

How can I calculate the center of an object relative to a focal point and a moving observer? [closed]

I'm developing an app that contains a 3D scene which the user can navigate. As the user moves it gives the illusion that you are browsing a real landscape but for the illusion to work I need to know ...
0
votes
4answers
78 views

Find a central force given the orbit

I've been trying to solve the following problem for a long time. Let's consider a particle of mass $m$ in $\mathbb{R}^3$ with polar coordinates $(r,\theta,\phi)$. The particle moves on the orbit ...
0
votes
2answers
53 views

Kinematic sign convention

For example, if I drop a ball from a $50$ meters building, then I will consider the ground is $0$ meter downward is positive ( which makes gravity positive, downward velocity positive, etc) so ...
0
votes
0answers
48 views

Spherical coordinate versor problem [migrated]

I have to calculate $$ i_\rho \times i_\phi $$ it should be $$ i_\theta $$ but in my notes I have $$ - i _\theta $$ Which one is correct? How can I do this kind of operations without mistakes?
-2
votes
1answer
62 views

Length in polar coordinates

Say we are in 3 dimensions and use $(-++)$. If we have the metric $$ds^2=-dt^2+dr^2+r^2df^2(t),$$ then what is the third coordinate if the first two were $t$ and $r$? $$X^iX_i=-t^2+r^2+?$$
1
vote
0answers
51 views

Double dot product in Cylindrical polar coordinates - Strain Energy

I'm working with a problem in linear elasticity, and I have to calculate the strain energy function as follows: $$2W=σ_{ij}ε_{ij}$$ Where σ and ε are symmetric rank 2 tensors. For cartesian ...
-2
votes
2answers
46 views

How to know the Direction of the Acceleration Vector?

If the exercise doesn't give you the direction, how to know the correct one? Sometimes I assume its to the right and it was actually to the left, and I get everything wrong. Example here: How can I ...
6
votes
1answer
80 views

Curvilinear Coordinates and basis vectors

In these notes, $\frac{\partial \vec{r}} {\partial q_i}$ is stated to form a basis set for the vector space. How does this happen? Also, how does one justify this equation from Goldstein's ...
1
vote
1answer
48 views

How can I find the motion equations of the 2-dim harmonic oscillator?

First of all: I am no physicist, so I am rather helpless. I need to find the moving equations of the 2-dim. harmonic oscillator. If it is possible it should be rather elementary, because, as I said, ...
1
vote
1answer
80 views

Which symmetry for which distance function

For evaluating the electric field of some charge distribution one can use $$\phi(r):= \frac{1}{4 \pi \varepsilon_0}\int_{\mathbb{R}^3} \frac{\rho(r')}{||r-r'||_2} dr'.$$ My question is: What symmetry ...
0
votes
1answer
49 views

Inconsistent integral and distance in spherical coordinates

I am currently studying this problem: 14 b) There you see an integral $$A(r) = \int f(\theta) (-\sin(\phi), \cos(\phi),0) d \Omega$$ where $f$ is the function containing all the rest of the integrand ...
-1
votes
1answer
74 views

Prove one of the following trajectories is circular

In his classical mechanics lecture, Prof Susskind gives a short exercise, which I "feel" is very simple, but don't know where to start with. The question is: "There is a coordinate system ...
0
votes
0answers
62 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 ...
1
vote
0answers
72 views

About the proof of the second Bianchi Identity

The second Bianchi Identity is $$ \nabla_{[a}R_{bc]de}=0 $$ As far as I know, the proof (say, Walfram Mathword) start by stating the representation of Riemann tensor in local inertial coordinates $$ ...
2
votes
2answers
54 views

Show that two families of curves are orthogonal (without using orthogonal trajectories)

I'm reading through Hartle's General Relativity and came across this question: Consider the following coordinate transformation from rectangular coordinates $(x,y)$, labeling points in the plane ...
1
vote
2answers
255 views

Calculating the electric potential in cylindrical coordinates from constant E-field

I am having so much trouble with this problem. I feel like I shouldn't be, but I am. A uniform electric field, $\vec{E} = E_0\hat{x}$. What is the potential, expressed using cylindrical ...
0
votes
0answers
71 views

Transforming components of the angular momentum operator

Let me introduce the problem: In a two electron fixed nucleus problem the "body" is the atom, whose electrons are located relative to the nucleus by the coordinates $r_1$ and $r_2$, and the angle ...
1
vote
1answer
218 views

Optimal selection of generalized coordinates in Lagrangian system

EDITED: The number of bonds is actually 2, not 1 (look at edit history). Fixed for archiving purposes. Problem: The edge A of an homogeneous rod (of length $\ell$ and mass $m$) is performing a smooth ...
2
votes
2answers
198 views

Exercise about Lagrange-Euler equations

I'm solving an exercise about the Lagrange-Euler equations, that states the following: Let $\gamma (t) = \{ (t,q) : q = q(t), t_0 \leq t \leq t_1\}$ be a curve in $\mathbb{R} \times \mathbb{R}^2$. ...
4
votes
1answer
125 views

Integrating Radial Vector Fields

Given a integral $$\int_vd^3{r} \;\vec{r}\;\rho(r)$$ and How do you convert it to spherical coordinate system, noting that $\rho(r)$ is indeed as it is without vector, i.e. it is spherically symmetric ...
0
votes
1answer
56 views

Parametric equations of a hypersurface

In light-front QFT, in the Minkowski space, we define a hypersurface, $\Sigma_+ : x^3+ x^0 = 0 $. How can I write its parametric equations?
2
votes
2answers
2k views

Expression of kinetic energy in polar coordinates

Expression for kinetic energy in Cartesian coordinate: Expression for kinetic energy in polar coordinate (applying the transformation of coordinates): Why can't we express it in the following ...
2
votes
1answer
168 views

Expression of electrostatic field

An electrostatic field is characterized by the fact that it depends only by $r$, isn't it? If it is true, I don't understand why this expression, given in cylindrical coordinates, $${\bf ...
0
votes
1answer
261 views

Rotating point in 3D space by Unknown rotation vector [closed]

I have a random point defined by: int x = rand.nextInt(9)-4;//-4 to +4 int y = rand.nextInt(4)+2;//+2 to +5 int z = rand.nextInt(9)-4;//-4 to +4 Y happens to be ...
1
vote
1answer
287 views

Electromagnetic Tensor in Cylindrical Coordinates

I understand that the Electromagnetic Tensor is given by $$F^{\mu\nu}\mapsto\begin{pmatrix}0 & -E_{x} & -E_{y} & -E_{z}\\ E_{x} & 0 & -B_{z} & B_{y}\\ E_{y} & B_{z} & ...
1
vote
1answer
71 views

Can we change frame of reference twice in a single problem?

My question has an inclined plane of mass $M$ and simple block kept on it, of mass $m$ (Both on a table). All surfaces are friction-less. Both of the objects would move, block down the incline and ...
1
vote
1answer
81 views

How to add magnitude data in an ENU coordiante system

I have water velocity data taken in an ENU (East, North, UP) or XYZ coordinate system. The data is contained in 3 columns like this: ...
1
vote
5answers
2k views

How to get the angle needed for a projectile to pass through a given point for trajectory plotting [closed]

I am trying to find the angle needed for a projectile to pass-through a given point. Here is what I do know: Starting Point $(x_0,y_0)$ Velocity Pass-through point $(x_1, y_1)$ I also need to ...
2
votes
0answers
2k views

Rotate vector in spherical coordinates

I have two arbitrary vectors $\vec{x}$ and $\vec{x}'$ given in spherical coordinates $(|\vec{x}|=x,\theta,\phi)$ (as convention I take the "physics notation" given on Wikipedia ...
0
votes
1answer
1k views

How to get the gradient potential in polar coordinate

In polar coordinate, $$\nabla U = \frac{\partial U}{\partial r}\hat{\mathbf{r}} + \frac{1}{r}\frac{\partial U}{\partial \theta}\hat{\mathbf{\theta}} .$$ Can anyone show me how to get this result?
0
votes
2answers
212 views

How was transformed an integral below?

I know how transform an integral below, $$ \iint f(\mathbf v_{1})f(\mathbf v_{2})d^3\mathbf v_{1}d^3\mathbf v_{2}, $$ using relative speed coordinates: we just use $$ m_{1} \mathbf v_{1} + ...
0
votes
1answer
3k views

Conversion of motion equation from Cartesian to Polar coordinates: Is covariant differentiation necessary?

I have earlier posted the same question here on math stackexchange but without any answer. As the question concerns tensors, I guess that I have come to the right ...
3
votes
1answer
3k views

Force from point charge on perfect dipole

Have a point charge and a perfect dipole $\vec{p}$ a distance $r$ away. Angle between $\vec{p}$ and $\hat{r}$ is $\theta$. Want to find force on dipole. I'm having more than a little difficulty ...
-1
votes
1answer
569 views

How do I express the Kepler general orbit $r(\phi)$ in rectangular coordinates?

How do I express the Kepler general orbit $r(\phi)$ in rectangular coordinates? I use the identities $x=r\cos\phi$, $y=r\sin\phi$, and $r^2 = x^2 + y^2$, but I block at some point.
1
vote
3answers
8k views

Find radius of curvature, given a velocity vector and acceleration magnitude?

The particle P moves along a space curve. At one instant it has velocity $v = (4i-2j-k)$ $m/s$. The magnitude of the acceleration is 8 $m/s^2$. The angle between the acceleration and the velocity ...
1
vote
1answer
715 views

converting force from spherical to Cartesian coords

So I am working on my assignment, and have a question about converting coordinates. I dont know whether I should ask here or the math SE, so lets give it a try here. The force in question is ...