Questions related to mathematical physics which include application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories

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Help with a 3-body problem

If I have three particles with masses $ m_1, m_2, m_3$ with their respective position vectors $ x_1, x _2, x_3 $ and their speeds $ v_1, v_2, v_3 $ how could I find a parametric function that would ...
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1answer
42 views

How to solve for multiple unknowns using substitution?

$R_1$, $R_2$, $R_3$, $R_4$, $R_5$ and $V_6$ suppose to be 'known' values. $$\frac{V_{n_1}}{R_1} + \frac{V_{n_1}-V_{n_3}}{R_2} + i_6 = 0$$ $$ \frac{V_{n_2}-V_{n_3}}{R_4} + \frac{V_{n_2}-V_{n_4}}{R_3} ...
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1answer
95 views

I want to learn math from zero

I finished high school 2 years ago and now I'm stuck in a university in Turkey. I am interested in learning precalculus, discrete mathematics, physics and chemistry. Question: I need to learn math ...
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1answer
21 views

Objects sliding on a frictionless surface

An object with the mass 2 kg slides on a frictionless surface. When the velocity of the object is h, the object is subjected to a force (air resistance) that's $5v^2$ N. Apparently the equation is ...
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1answer
19 views

Double-check my answer in calculating gravitational potential energy [on hold]

"A satellite with a mass of 200kg maintains its orbit at an altitude of 300km above the Earth's surface. The Earth has a radius of $6.38 * 10^6m$ and a mass of $5.97 * 10^24$" I was told this was the ...
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24 views

Stadium billiard reflection angles

Given a boundary and a massless particle with constant velocity with a certain direction, a billiard consists of an experiment where the particle collides with the walls conserving its velocity ...
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0answers
37 views

Interstellar's Gargantua (Black Hole) Equation [on hold]

I don't really know if this is a physics, computer science or mathematics question so kindly excuse me if I posted it at the wrong place. I want to know what was maths/equations that were used to ...
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1answer
29 views

Partial Differentiation in Statistical Mechanics

I am damn struggling with basics in here. I know that $U=U(N,V,T)$ and $z=z(N,V,T)$ so that $N=N(z,V,T)$. Now, I want to do partial differentiation using chain rule involving three variables so that I ...
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0answers
62 views

Why are quaternions useful? [duplicate]

What I mean is why are they used basically where they are used? Listing some advantages of using them would be better. I am taking a mechanics course where a teacher mentioned them in a discussion ...
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60 views

Speed of light and relativity [on hold]

I have been thinking about the speed of light and relativity and I have a question I would like to get an answer to. If two vehicles are side by side and they start moving forward at 100 mph and ...
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0answers
53 views

Physical or geometric meaning of the trace of a matrix

The geometric meaning of the determinant of a matrix as an area or a volume is dealt with in many textbooks. However, I don't know if the trace of a matrix has a geometric meaning too. Is there ...
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Examples of useful, insightful, and interesting hand-waving

I am really amused by the answers to this question on "Most harmful heuristic" posed on MathOverflow, from which I've benefited a lot. However, it seems to me that some hand-waving may be really ...
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22 views

physics question [closed]

A car travels 11.5 km west at a speed of 40 km/h, then travels 15.6 km south at a speed of 50 km/h and finally travels 19.1 km east at a speed of 45 km/h. What is the magnitude of the average velocity ...
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1answer
38 views

Interchange of derivatives

Given Euler-Lagrangian equation $$\frac{d}{dt}\frac{\partial L}{\partial \dot q}-\frac{\partial L}{\partial q}=0$$ Can I equivalently write as $$\frac{\partial \dot L}{\partial \dot q}-\frac{\partial ...
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2answers
39 views

How much thrust is required to move a boat of 120 kg / 265 pounds to a speed of … [closed]

How much thrust is required to move a boat of 120 kg / 265 pounds to a speed of 10 km / 6 miles per hour in 7 seconds. I found the following: http://en.wikipedia.org/wiki/Thrust-to-weight_ratio ...
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3answers
44 views

Work done to fill up a spherical tank

A spherical tank of radius $12$ feet is $40$ feet above the ground. How much work is done in pumping water into the tank until it is full? I obtained $$ w= \int_{16}^{40}[12^2-(40-y)^2y] \, dy. ...
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1answer
21 views

mechanics piston problem involving rotational motion.

The above figure shows a piston driving a crank OP pivoted at the end $O$. The piston slides in a straight cylinder and the crank is made to rotate with constant angular velocity $ \omega $. Find ...
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3answers
59 views

Geometric Algebra/ Calculus for Physics

I don't know if this would be a better question for physics.SE, but I'll try here first: There is at least one good book on classical mechanics using the geometric algebra/ calculus (GA): New ...
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2answers
84 views

How did they solve for a here?

Consider the following algebraic steps: $$ F - (M_1 a + \mu_k M_1 g) - \mu_k M_2 g = M_2 a $$ $$ F - \mu_k M_1 g - \mu_k M_2 g = (M_1 + M_2) a $$ $$ a = \frac{F - \mu_k M_1 g - \mu_k M_2 g}{(M_1 + ...
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0answers
29 views

Solving 2 equations (Projectile motion)

The question is from Physics, but all I need is help on solving maths. So basically, i am trying to find out the optimal angle for projectile motion from a certain height and I end up with these two ...
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0answers
17 views

How to describe the motion of a mass point?

Consider a mass point moving around a fixed point on a circle with radius $r$ with constant angular velocity $ω$. At a certain moment of time, the connection is removed, and the point mass is flying ...
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2answers
53 views

How to find $\theta$ at which $d$ is the maximum possible?

I have an equation: $$d=\dfrac{v\cos \theta}{g}\left(v \sin \theta + \sqrt{v^{2} \sin^{2}\theta + 2gh} \right),\ g≈9.81 \dfrac {m}{s^{2}}$$ How to find $\theta$ at which $d$ is the maximum possible? ...
6
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1answer
85 views

Dirac Gamma matrix identity

In my library's (old -- 1996) copy of Peskin and Schroeder, there's an identity I'm struggling to prove. In my copy it occurs on page 42, between equations 3.28 and 3.29, but I don't know how well ...
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1answer
34 views

How do I calculate the centripetal force?

In this experiment, a brown rubber weighs 42.2 grams and was spun at a velocity of 4.66m/s with a radius of 40cm and masses of 200g...the answer should be about 1.96N and I got 2.3. Can someone ...
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1answer
12 views

$\int_C (\alpha x, -\alpha y) . dr = 0$ where C is the unit circle

Circulation is given by $$\int_C u . dr$$ I want to show that the circulation around the unit circle is $0$ for $u = (\alpha x, \alpha y)$. Ie. $$\int_C (\alpha x, -\alpha y) . dr = 0$$ How would ...
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2answers
115 views

Is “mixed math” a useful way to learn math?

I was reading a book about how mathematics was taught in Cambridge in the 19th century, and it struck me how much physics was included in the syllabus, and it wasn't optional but everyone had to learn ...
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1answer
27 views

Work required to pump water out of tank in the shape of a paraboloid of revolution

This is the problem I have been assigned: A water tank has the shape of a paraboloid of revolution: its shape is obtained by rotating the parabola $y=x^2/4$, for $0\le x\le 4$, around the ...
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33 views

intersecting point of two lines

The circle has R radius and and ellipse is intersecting the circle. I need to findout $x_c$ and $y_c$, which is the midpoint of the 2 intersected point of ellipse.Line 3 is the tangent of the ...
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1answer
42 views

A formal justification for this “physicism”?

I gave a presentation for a seminar class yesterday on Fourier analysis, and introduced the sawtooth function as a counterexample, for a function whose Fourier series is not termwise differentiable. ...
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1answer
39 views

Tough second order differential equation2

I have asked similar question before but it turns out that the $E_0$ depends on (r,z). It makes the solution complicated. Any comments appreciated. ...
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8 views

Proving susceptibility in Lorentz Model satisy Kramers-Kronig relations

My instructor asked me to prove that the real and imaginary parts of the electric susceptibility derived from Lorentz Model satisfy the Kramers-Kronig relations using the residue theorem. The problem ...
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9 views

Potentials and Markov Processes

Given a resistive electrical circuit $G$, i.e. a graph with nonzero weights attached to each edge whose reciprocal we call the "resistance," we can define a reversible markov chain on the graph, ...
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3answers
49 views

$\vec{r} \times (\vec{\omega}\times \vec{r})=r^2\vec{\omega}-(\vec{\omega}\cdot\vec{r})\vec{r} $

Show (in cartesian coordinates) that $\vec{r} \times (\vec{\omega}\times \vec{r})=r^2\vec{\omega}-(\vec{\omega}\cdot\vec{r})\vec{r} $ I am not really sure how to calculate this. Do I just assume ...
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0answers
27 views

Ode with Piecewise function

We can write this $$12x"+36x'+48x=f(t)$$ my main problem is how to solve this non-homogeneous ODE I know how to do this as 2 different ode unfortunately its not in a syllabus which doesn't use ...
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1answer
28 views

Heat equation fundamental solution

The following is from a book of PDEs and I have cannot seem to figure out a particular step in it with regard to the derivation of the fundamental solution of the heat equation. I have highlighted it ...
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0answers
7 views

Converting a boolean expression into CNF and DNF

Is there any systematic way to convert the following boolean expression (QUBO) into CNF or DNF? Here, $x_1, \ldots, x_n \in \{0, 1\}$, $a_1, \ldots, a_n \in \mathbb{Z}$ and $b_{1,1}, \ldots, b_{n,n} ...
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65 views

All $f(x)$ on $[0,1]$ such that center of mass of the function (uniform density) is on its graph

So, as the title describes, I'm trying to find a way to express all $y=f(x)$ differentiable on $[0,1]$ such that the center of mass of the function, assuming it has uniform density, will be a point on ...
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1answer
15 views

Angular momentum superposition

I am doing a space simulation. I have a spaceship and this spaceship has engines that don't push the spaceship through its center of gravity. These engines can therefore give the spaceship angular ...
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1answer
35 views

Equations of Motion of a Satellite

I'm working on a control problem where I need to know the equations of motion for a satellite orbiting the earth about a central axis. Using Newton's second law, I was able to show that ...
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1answer
37 views

Calculation of a spread light on a surface

Suppose we have a light of power $P$ distributed on a plane $(x,y)$. The distribution of the power is of the form: $$P=f(x,y)$$ If we have a lens conjugating every point of the plane $(x,y)$ in ...
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1answer
74 views

Solve $\int_0^T f(t) dt =1$ for T.

I have to solve this equation for a physics problem and I don't know where to start: $$\int_0^T f(t) dt =1 \quad\text{and}\quad f(T)=C$$ Where $T>0$, $C>0$ and $f(t)>0$ we can suppose that ...
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0answers
31 views

Computing the Initial Velocity of an orbiting body [migrated]

I'm working on a simulation program that replicates the movement of planets around a large celestial body (the sun). This is a three dimensional simulation that uses vectors. At present, I'm ...
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0answers
15 views

Approximation for uniform load on parabolic cable along its arc length

I am doing analysis for cable structures. Let's say that the cable stretches from point A to point B and carries a vertical ...
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2answers
44 views

Is it possible to build a fiber bundle whose fibers are different? (Or we should not call it a fiber bundle?)

Suppose there is a fiber bundle $E$. The base space is $M$ so that $\pi:E\rightarrow M$ is the projection. By the definition, the bundle has a typical fiber $F$ such that the local trivialization over ...
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1answer
37 views

Is there always an equilibrium point in a field?

For instance, considering a set of planets represented as point masses that create a gravitational field, will there always, no matter what set of points, be a place where I can stand with no net ...
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1answer
49 views

Derivation of Simple Projectile Motion with Drag

Given the initial velocity $v_0$ and angle $\theta$ of a projectile on the ground, using Newton's second law and the acceleration due to gravity $\mathbf g=\left\langle0,-g\right\rangle$, I was able ...
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0answers
47 views

Calculating Hydrodynamic Interaction Tensor

I'm a bit of a newbie when it comes to Tensor calculus. Please excuse me as I learn... Given the Oseen tensor, $\mathbf{T}(\mathbf{R}) = (8\pi \eta R)^{-1} \left[ \mathbf{I} + ...
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0answers
35 views

Calculating force per unit width

Question: A line source of strength $2πm$ is located a distance $a$ above a horizontal plate. Find the force per unit width on the plate, ignoring gravity and taking the pressure below the plate to be ...
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0answers
39 views

Kinematics of gravity in a non uniform field

I am a first year physics student. I am trying to figure out how to compute position in terms of time for an object falling through non uniform gravity towards the earth, and by extension towards any ...
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8 views

How to solve a factorized Helmholtz equation?

I am reading a paper on optics an in appendix A2 they split the Helmholtz equation into two parts and write down the solution for one of those parts (link). Helmholtz Equation where the Laplacian is ...