[tag:classical-mechanics] entails the study of the trajectory of bodies under the influence of forces. More specific subtopics are: [tag:newtonian-mechanics], [tag:lagrangian-mechanics], [tag:hamiltonian-mechanics] for point particles and [tag:fluid-dynamics], [tag:statistical-mechanics] and ...
0
votes
1answer
207 views
Ball rolling down an inclined plane going in to a loop
I apologize if this question is not up to par.
When I was doing exercises in basic mechanics I checked the answers and I can't seem to find what I'm doing wrong.
Suppose we have a ball with mass $m$ ...
2
votes
2answers
135 views
Rigid body dynamics of tossing of a coin
While tossing a coin, it is commonly experienced that you get a head, if you toss it up with the head side up, and a tails if you toss with the tails side up. Is there a mathematical proof of this ...
1
vote
2answers
132 views
Small Oscillations and matrices: suggestion about text
I'm undergraduate and I'm looking for a text about Small Oscillations in which matrices are used. Could you suggest me a book or a PDF file?
5
votes
4answers
220 views
Non-Integrable systems
Integrable systems are systems which have $2n-1$ time-independent, functionally independent conserved quantities (n being the number of degrees of freedom), or n whose Poisson brackets with each other ...
0
votes
0answers
47 views
Finding an efficient strategy for walking
Let's say you are already walking at a maximally efficient combination of pace and stride (or $\omega$ and $X_0$ I guess) but you need to reach your destination faster. Should you increase/decrease ...
2
votes
1answer
78 views
Flat poster on a wall gaining curvature over time
Assuming you have a flat poster with no curvature, why is it that when you pin it to the wall (with thumbtacks) it gains curvature as seen in the picture below. When I put the poster up it was ...
2
votes
1answer
209 views
Two masses with interacting forces and an external force
Two masses in 3d space attract each other with a potential relative to the distance between them. There is also an external force on each particle based on the distance from a origin. I want to find ...
3
votes
2answers
780 views
Normal Forces and Ferris Wheels
At the moment, I am reading an example problem regarding what was alluded to in the title. In this example problem, they say, "Based on experiences you may have had on a ferris wheel or driving over ...
1
vote
1answer
78 views
Why does leaning back make a kicked ball go higher?
It's relatively common knowledge that when one kicks a football, if they lean back the ball usually goes higher, and if they lean forward slightly it goes at a more desirable height.
Why does leaning ...
11
votes
3answers
261 views
Car accident, put in park or neutral?
I was waiting on a red light the other day and was wondering.
If I'm in my car, not moving and I see a car that's going to hit me from behind. Would I (my body) be safer if I put on the break or if ...
0
votes
1answer
135 views
Generalized momentum conjugate and potential $U(q, \dot q)$
On Goldstein's "Classical Mechanics" (first ed.), I have read that
if $q_j$ is a cyclic coordinate, its generalized momentum conjugate $p_j$ is costant.
He obtained that starting from Lagrange's ...
-1
votes
1answer
79 views
Question about de Broglie Waves?
Is photon interaction , electrostatic interaction outside the nucleus and gravitational interaction is all due to electromagnetic waves ? and CAN be identified as with the de Broglie waves ?
I ...
1
vote
0answers
61 views
Is the geometric formulation of Hamiltonian mechanics really necessary? [duplicate]
Possible Duplicate:
Why is the symplectic manifold version of Hamiltonian mechanics used in Newtonian mechanics?
I was sitting around with some friends the other day trying to come up with ...
1
vote
3answers
89 views
Reference for the predictability of rigid body dynamics
I'm looking for a reference, journal article, paper, etc. that supports the idea that classical mechanics, in particular rigid body dynamics, is largely predictable.
A view coming from the background ...
1
vote
2answers
260 views
To find whether a particle is in equilibrium or not
Actually the following question came in an exam i gave yesterday. I know the site does not allow home-work type questions, but as I am having a conceptual problem in solving the question, I am posting ...
0
votes
0answers
175 views
Classical Mechanics: A particle move in one dimension under the influence of two springs [closed]
A particle of mass $m$ can move in one dimension under the influence of two springs connected to fixed points a distance $a$ apart (see figure). The springs obey Hooke’s law and have zero unstretched ...
0
votes
1answer
368 views
Determine the maximum height a pump can suck up water
I am working on a homework problem that presents the scenario of trying to raise water from a small reservoir of depth 8 m whose surface is 25 m below a pump that can maintain a pressure differential ...
0
votes
1answer
101 views
Non-relativistic Kepler orbits
Consider the Newtonian gravitational potential at a distance of Sun:
$$\varphi \left ( r \right )~=~-\frac{GM}{r}.$$
I write the classical Lagrangian in spherical coordinates for a planet with mass ...
2
votes
1answer
187 views
How to explain the different forms of the Hamilton-Jacobi equation?
In Arnold's Mathematical Methods of Classical Mechanics, he derives the Hamilton-Jacobi equation (HJE) using a generating function $S_1(Q, q)$ to get
$$
H\left(\frac{\partial S_1(Q, q)}{\partial q}, ...
3
votes
3answers
231 views
When Hamiltonian and the total energy are the same
In which condition, the Hamiltonian is the same as the total energy of the system, or say $H=T+V$?
1
vote
3answers
354 views
Conservation of energy in objects at terminal velocities
In vacuum, object free falling under gravity, the sum of Gravitational Potential Energy(GPE) and Kinetic Energy (KE) is a constant. The GPE is a decreasing side of a quadratic and KE is a increasing ...
5
votes
1answer
119 views
The notion called aether
I am trying to learn relativity theory and going through an introductory text on special relativity. I stumbled on the Michelson-Morley experiment. The book claims (accounts) that the result of this ...
1
vote
1answer
140 views
Clarification on a Goldstein formula steps (classical mechanics)
At page 20 of Classical Mechanics' Goldstein (Third edition), there are these two steps given between eqs. (1.51) and (1.52):
$$\sum_i m_i \ddot {\bf r}_i \cdot \frac{\partial {\bf r_i}}{ \partial ...
3
votes
1answer
99 views
What are the fields in this problem?
In problem 3 of chapter 2 of Landau Lifshitz "Mechanics," I don't understand the meaning of the fields as defined in the following statement:
Which components of momentum and angular momentum are ...
0
votes
0answers
67 views
What are the details of this variational calculus solution?
This answer includes the problem:
Suppose you have a 2-d bullet going very fast through a 2-d gas. The gas molecules reflects specularly off the bullet, making glancing collisions. What shape of ...
0
votes
2answers
141 views
Is it reasonable for a heavy door to “open by itself” (ie from differences in air pressure) if it had already been slightly ajar?
If you consider a basically uniform massive door (say, 300 N) where there is some coefficient $\mu_{s,k}$ of static and kinetic friction between the thing on the inside of the door, and where the ...
4
votes
2answers
184 views
Landau Mechanics: why does adding Lagrangians remove the indefiniteness of multiplying each Lagrangian by a different constant?
In Landau Mechanics (third edition page 4), why does adding Lagrangians of two non interacting parts remove the indefiniteness of multiplying each Lagrangian by a different constant?
If both systems ...
-4
votes
1answer
83 views
Is there a formula to measure how much something would bend with weight on it? [closed]
Is there a formula to measure this?
If you know please share, thanks.
3
votes
1answer
173 views
Can I find a potential function in the usual way if the central field contains $t$ in its magnitude?
I'm working on a classical mechanics problem in which the problem states that a particle of mass $m$ moves in a central field of attractive force of magnitude:
$$F(r, t) = \frac{k}{r^2}e^{-at}$$
...
3
votes
1answer
332 views
Coriolis force in free fall
Does the coriolis force has any measurable effect in free fall from large heights?
Take for example the sky diving experiment by F. Baumgartner who started from a height of about 40 km above New ...
6
votes
2answers
214 views
What are the reasons for leaving the dissipative energy term out of the Hamiltonian when writing the Lyapunov function?
I have a problem with one of my study questions for an oral exam:
The Hamiltonian of a nonlinear mechanical system, i.e. the sum of the kinetic and potential energies, is often used as a Lyapunov ...
1
vote
1answer
718 views
What is the relationship between mass, speed and distance of a planet orbiting the sun?
After reading this fascinating story about a new exoplanet, I was wondering about how mass, speed and distance determine a circular orbit of a planet around a star.
Given the mass of the sun and ...
1
vote
2answers
207 views
Charge, velocity-dependent potentials and Lagrangian
Given an electric charge $q$ of mass $m$ moving at a velocity ${\bf v}$ in a region containing both electric field ${\bf E}(t,x,y,z)$ and magnetic field ${\bf B}(t,x,y,z)$ (${\bf B}$ and ${\bf E}$ are ...
3
votes
2answers
414 views
Differences between classical, analytical, rational and theoretical mechanics
Can you explain me what are the differences between the four following subjects?
analytical mechanics
rational mechanics
classical mechanics
theoretical mechanics
0
votes
0answers
39 views
Could you help and check my four easy dynamics tasks? [closed]
So I have four tasks to do and I have a guess for some of them but would greatly appreciate if you could help me be sure of it or clarify what I don't understand.
A car covers 2000m in 2 minutes and ...
1
vote
1answer
141 views
Problem in Hamiltonian
I need to elaborate the equation ,and need to know what is the physical significance and how matrices will manipulate in the equation $$
\hat{H} = (\hat{\tau_3}+i\hat{\tau_2})\frac{\hat{p}^2}{2m_0}+ ...
0
votes
1answer
177 views
Determining friction for unbalanced wheel to roll without sliding
I'm trying to model a weighted wheel rolling without slipping. I understand that friction, by virtue of being an off-center force, affects both linear and angular acceleration. So my train-of-thought ...
0
votes
0answers
21 views
What will be my motion inside earth [duplicate]
Possible Duplicate:
If it was possible to dig a hole that went from one side of the earth to the other
Suppose I drill a hole in earth through the centre and out from the other side. If I ...
3
votes
3answers
235 views
Particles as a limit of classical field theory
A common academic exercise has been to show that classical mechanics is a limit of quantum mechanics, usually by putting $\hbar \rightarrow 0$.
Similarly is it possible to show that a limit to field ...
1
vote
0answers
26 views
reference request: Classical Mechanics as an Application to Smooth Manifolds [duplicate]
Possible Duplicate:
Classical Mechanics for Mathematician
Last time I asked a question, but it does not sound specific. I am currently taking graduate topology class (using Lee's ...
0
votes
0answers
258 views
Torque required to rotate a cement mixer..? [closed]
I need to design a motor to rotate a cement mixer which should mix one cubic meter. So, I calculated the required volume to be 1600 liters as it is an horizontal cylinder. Consider that the mixer ...
2
votes
1answer
1k views
Determining the center of mass of a cone
I'm having some trouble with a simple classical mechanics problem, where I need to calculate the center of mass of a cone whose base radius is $a$ and height $h$..!
I know the required equation. But, ...
2
votes
0answers
93 views
Eternal clocks and 4D spacetime crystals
There was a recent article about the creation of 4D spacetime crystals based on recent theory proposed by Frank Wilczek. This theory is based on breaking time translational symmetry which basically ...
1
vote
1answer
91 views
Physics of homebrewing heat exchangers
In homebrewing on of the key steps when brewing with extract is to rapidly chill the wort from boiling temperatures to about 80F in 30 min. This is needed to reduce risk of environmental ...
1
vote
1answer
65 views
Rigid body/moment of inertia problem
I have a homework assignment about rigid body dynamics. Take a disc of radius $r=2m$ with uniform mass density $\rho=1$ $kg/m^2$ in the x-y plane, resting in an inertial frame. At some instant, a ...
1
vote
1answer
133 views
How is the singularity in Newtonian gravity resolved?
In Who's afraid of a Black Hole? at time ~20:38, Michio Kaku makes a claim that $1/r$ when $r=0$ equals $\infty$ and when physicists see the $\infty$ they see a monstrosity. Coincidentally, Newton's ...
2
votes
2answers
251 views
Meaning of subscript in $V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$
This is probably a simple question, but what does the subscript $0$ mean in the following expression?
$$V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$$
0
votes
1answer
40 views
If a people happen to be fall into the ocean from 50m high, then would the diving pose in the olympiad make less percussion
If a people happen to be fall into the ocean from 50m high, then would the diving pose in the olympiad make less percussion then the leg going first into the water so that the body receive less ...
14
votes
4answers
455 views
Is the principle of least action a boundary value or initial condition problem?
Here is a question that's been bothering me since I was a sophomore in university, and should have probably asked before graduating:
In analytic (Lagrangian) mechanics, the derivation of the ...
1
vote
1answer
141 views
Hamiltonian Flow Map
I'm reading this article and am struggling with some of the terminology. What is the flow map for a Hamiltonian system? I'm looking for a rigorous definition really!
Many thanks in advance.
