0
votes
1answer
12 views

How to find time it takes for an object to slide on an incline ramp [on hold]

So I hope I am asking this question in the correct spot. Here is my question: if there is an incline at $70$ degrees, the object's friction is $\mu = 0.1$, and the incline is $1$ meter long, how long ...
1
vote
1answer
60 views

Mathematics/Mechanics Problem

I would like to ask you if anybody could help me with this problem. So far i know that the positions where B and A have to meet are at distances L and L+2r
1
vote
1answer
63 views

Calculating a double pendulum

consider the following situation of a double pendulum. We found the moving equations as $$ \ddot{\theta_1}=-L_1\sin\theta_1 + \frac{m_2}{m_1}\cos\theta_2\sin(\theta_2-\theta_1),\\ ...
-1
votes
1answer
38 views

The phase plane and potential energy

I think I have spotted a mistake in my notes, however I need help verifying my assumption: I am given the equation: $d^2s/dt^2=-s$ m=1 for simplicity I have recast it at a first order system: ...
0
votes
2answers
60 views

Time period for simple pendulum without trigonometry

The time period for simple pendulum formula that is $t = 2\pi \sqrt{\frac{l}{g}}$ is valid only for $15^\circ$ of amplitude. Why not more than that? How do I explain this someone who has just been ...
-1
votes
2answers
97 views

Sketching phase portraits [closed]

I am trying to answer this question: I would like to know how I go about drawing a phase portrait. All of the examples in my notes are simply the solution with no explanation, and this method of ...
4
votes
2answers
114 views

A problem about symplectic manifolds in Arnold's book

There is a problem in Arnold's Mathematical Methods of Classical Mechanics which says that: Show that the map $A: \mathbb{R}^{2n} \rightarrow \mathbb{R}^{2n}$ sending $(p, q) \rightarrow (P(p,q), ...
0
votes
1answer
19 views

When finding the frequencies of normal modes, can you have a negative frequency?

Do you simply just consider the positive solutions? I tried a google search but didn't find anything quickly. The work I am studying is Lagrangian systems.
0
votes
0answers
41 views

Finding angular momentum about the center of mass?

If we have a couple of particles of an equal, unknown mass: $r_{+} = (c + e^{-Bt} \cos({\theta}))\textbf{x} + (d + e^{-Bt} \sin({\theta}))\textbf{y}$ $r_{-} = (c - e^{-Bt} \cos({\theta}))\textbf{x} ...
0
votes
0answers
25 views

Lagrangian of a pendulum inside af disc

I'm currently struggling with a mechanical problem, where I need to find a relationship between the two angles in a mechanical system. The two equations of motions were derived using the Lagrange ...
0
votes
1answer
21 views

Time taken to reach height below initial point

I am trying to solve the following. It is in my notes, I believe I need to solve: $-H = v_0cos\alpha*t\bf{j}$$+(v_0sin\alpha*t-gt^2/2)\bf{k}$ as a quadratic equation? If so, how do I solve a ...
0
votes
0answers
85 views

Line Integral Problem best or easier solved using geometry?

Does anyone have any recommendation on a line integral problem involving vector fields (aka work) such that evaluating the resulting line integral using parameterization would be significantly ...
0
votes
1answer
60 views

Relative velocities of a boat and a stone thrown by the boat.

Question: A police boat is chasing a boat with criminals along a straight river by moving against the stream. The speed of the river stream is 3 miles per hour, the speed of the boat with ...
1
vote
1answer
189 views

Drawing a graph of potential energy as a function of displacement $x$.

The water density is changing linearly with the displacement x>0, i.e. $\rho = \rho_0 + kx$, where $\rho$ > 0 and k>0. Also, assume that $\rho_0V < m $. I know that potential energy, $V = - \int ...
1
vote
1answer
131 views

Solving for Asteroid Orbit with Respect to Time

I am trying to create a differential equation with which I am can numerically solve to plot the orbit of an asteroid around Jupiter so far I have assumed the mass of jupiter is 0.001 of the mass of ...
1
vote
2answers
198 views

Derive the equation of motion from Lagrangian of a particle moving in an electromagnetic field

I really don't even know where to start with this question any help would go very very far. Thank you. A particle with charge $q$ moving in an electromagnetic field is described by the Lagrangian ...
1
vote
0answers
44 views

Particle in a Polya Vector field

For a given analytic function $H$ from $\mathbb{C}$ to $\mathbb{C}$, we define the Polya Vector Field to be $\bar{H}$. This then corresponds to a irrotational, conservative vector field on ...
2
votes
2answers
248 views

Calculating the linear output force a threaded rod and nut would produce based on the input torque

I would like to calculate the amount of linear thrust a threaded rod combined with a rotationally static nut would be able to produce based on the rotary force applied to the rod. The information ...
2
votes
0answers
449 views

Hard Differential Equation. Please help.

first of all I'm not a mathematician, so I apologize if any of my understanding and terminology isn't up to par. Also, I've never used this website (or any of these kind of question/answer) websites ...
0
votes
0answers
73 views

Close to giving up on this differential equation! Please help! [duplicate]

first of all I'm not a mathematician, so I apologize if any of my understanding and terminology isn't up to par. Also, I've never used this website (or any of these kind of question/answer) websites ...
1
vote
0answers
74 views

What is $\int \frac{\delta F}{\delta u} \frac{\delta G}{\delta v} \, dx \; $?

Given $F[u]$ and $G[v]$ are functionals of a real-valued function, what is $$ \int \frac{\delta F}{\delta u} \frac{\delta G}{\delta v} \, dx \quad ? $$ I have encountered such expressions for ...
3
votes
2answers
123 views

pressure in earth's atmosphere as a function of height above sea level

While I was studying the measurements of pressure at earth's atmosphere,I found the barometric formula which is more complex equation ($P'=Pe^{-mgh/kT}$) than what I used so far ($p=h\rho g$). So I ...
0
votes
1answer
328 views

Find the time at which a particle projected up an inclined plane, comes to rest?

A particle of mass $m$ is projected up a plane that is inclined at an angle $\alpha$ to the horizontal. At $t=0$, its velocity is $v_0$ and the coefficient of dynamic friction of the slope is ...
2
votes
0answers
559 views

Publication date for Michael Spivak - Physics for Mathematicians II?

I bought the book "Physics for Mathematicians I" by Michael Spivak (http://www.amazon.com/Physics-Mathematicians-Mechanics-Michael-Spivak/dp/0914098322), have worked through quite some chapters and ...
1
vote
0answers
36 views

Regularization theory

In order to remove the collision singularity in the equations of motion of the three dimensional two body problem, one defines the coordinate transformation $x_1=u_1^2-u_2^2-u_3^2+u_4^2$ $x_2=2(u_1 ...
7
votes
2answers
360 views

Euler-Lagrange equations of the Lagrangian related to Maxwell's equations

Clarification on Lagrangian mechanics would be much appreciated: Suppose $$L(\phi,\,\,\phi_{,i},\,\,A_i, \dot A_i)=|\dot A+\nabla\phi|^2-|\nabla \times A|^2-c\phi+d\cdot A$$ Are the corresponding ...
2
votes
4answers
164 views

Three ball-spring system

So here is a crazy problem for you all. Imagine there is a system of three balls in a line. The first and last balls have a larger mass M and the middle ball is a smaller mass m. Inbetwen the two ...
1
vote
0answers
127 views

Applications of mathematics to some kinds of sporting strategies

I am a rather newbie maths person. Haven't studied maths in a while and so not sure what things are called was hoping to get some information to push me in the right direction so I know what it is I ...
3
votes
2answers
107 views

Why is the landing footprint an ellipse?

Following the Curiosity landing I noticed that the possible landing site (the so-called 'landing footprint') was demarcated by an ellipse. Here is a picture of it: Now obviously such a footprint ...
8
votes
2answers
599 views

Fireworks under inverse-cube gravity

What is the path of a projectile under an inverse-cube gravity law? Imagine that the law of gravity was changed overnight from $F(r) = G m_1 m_2 / r^2$ to $F(r) = G' m_1 m_2 / r^3$. To be ...
1
vote
1answer
807 views

Moment of inertia - formula derivation: Missing $\frac{1}{2}$

I'm trying to deduce the formula of the moment of inertia of an object of rotation. The general formula for the moment of inertia is declared as: $$J=m*r^2 =\sum{m_i * r_i^2}$$ If I replace $m_i$ ...
54
votes
3answers
69k views

Teenager solves Newton dynamics problem - where is the paper?

From Ottawa Citizen (and all over, really): An Indian-born teenager has won a research award for solving a mathematical problem first posed by Sir Isaac Newton more than 300 years ago that has ...
0
votes
1answer
2k views

Maximum range of a projectile (launched from an elevation)

If a projectile is launched at a speed $u$ from a height $H$ above the horizontal axis, and air resistance is ignored, the maximum range of the projectile is $R_{max}=\frac ug\sqrt{u^2+2gH}$, ...
1
vote
1answer
305 views

How can I put the “3 body problem” mathematically?

I'm trying to put the 3 body problem mathematically. But I don't know how. I always get something reasonable, but I get something that is wrong.
2
votes
0answers
75 views

A lower positive bound on the number of closed orbits with given energy for a mechanical system

Let be given a mechanical system with configuration manifold $M,$ potential energy $V$ and kinetic energy $K$ corresponding to a riemannian metric on $M.$ Its dynamics is determined by the ...
2
votes
4answers
152 views

The motion of a system as a level set of the energy

Suppose we have a mechanical system with 1 degree of freedom, i.e. an ODE $$(1)\quad \ddot{q}+V^\prime(q)=0, $$ where $V \colon \mathbb{R} \to \mathbb{R}$ is some smooth function (potential ...
3
votes
1answer
629 views

Why does acceleration = $v\frac{dv}{dx}$

If we define $x$ = displacement, $v$ = velocity and $a$ = acceleration then I am used to the ideas that $a= \frac{dv}{dt} = \frac{d^2x}{dt^2}$ However I also understand $a=v \frac{dv}{dx}$. Can ...
1
vote
2answers
704 views

two-body problem circular orbits

I've been trying to google the answer to this question, but have had no luck, so I'm asking this question here. Let's say the origin is at (0, 0), body 1 with mass m1 is at (-r1, 0), and body 2 with ...
0
votes
1answer
191 views

slipping rod on moving truck

we have a truck in our game we have a rod against the wall of that truck, and we know the acceleration of truck when the rod start slipping... we just want to know what is acceleration of rod when it ...