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Questions tagged [classical-mechanics]

For questions on classical mechanics from a mathematical standpoint. This tag should not be the sole tag on a question.

Wikipedia says:

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. Besides this, many specializations within the subject deal with gases, liquids, solids, and other specific sub-topics. Classical mechanics provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light.

For questions on classical mechanics from a mathematical standpoint. This tag should not be the sole tag on a question. Examples of other tags that might accompany this include , , and .

2097 questions
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Question regarding Energy Conservation

A point mass $m$ is projected from the earth surface with speed $v_0$ and at an angle $θ$ above the horizontal. Assume that the gravitational acceleration is constant and has the absolute value $g$. Use energy conservation to show that, at any…
Mr Croutini
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Books on Mechanics

I was wondering if any of you know the names of some good books that give an introduction to langrangian and hamiltonian mechanics. I've finished kleppner and kolenkows introduction to mechanics and now would like to proceed to something a little…
john
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Harmonic Oscillator

I have a model which can be written as $$ \ddot \xi + r\dot \xi -\omega_0^2 \xi=0 $$ which is very similar to the harmonic oscillator (HO). …
Tengis
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Non-uniform rod Further Mechanics A-Level question from 1987

A non-uniform rod $AB$ has mass $6\mathrm{kg}$ and length $6L$. Its centre of mass is at a distance $L$ from $A$. One end of a light inextensible string is attached to the rod at A and the other end is attached to a small smooth ring $R$ of mass…
JCP13321
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Two points with zero velocity in some inertial frame move in a straight line

I've been trying to solve a problem in Arnold's Mathematical Methods of Classical Mechanics in which I'm supposed to show that given a mechanical system of two points such that they have zero velocity in some inertial frame then the motion of the…
prsdnt
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Lagrange equations of bar, 2 springs and a point mass

The system is placed on a vertical plane and composed of a homogeneous bar of mass m and length l which can only rotate about its baricenter at the origin. A particle P of mass m can move along the bar. Two springs are shown with constant $k>0$ The…
some_math_guy
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Are self-intersecting paths in configuration space allowed by the principle of least action?

The principle of least action in classical mechanics (with the Lagrangian formalism) states: Theorem. A path $\gamma$ between configurations $q_{(1)}$ at time $t_1$ and $q_{(2)}$ at time $t_2$ is a solution to the Euler-Lagrange equations…
giobrach
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Finding minimum distance traveled with specified deceleration from starting speed

Let's say there is an object flying around (in a straight line), which has a constant speed $v$ and zero acceleration. In some moment I can apply a constant deceleration $a$ to that object and I need to find a distance $d$ which will be traveled…
AgentFire
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Inertia tensor for a spherical shell

I'm asked to compute the inertia tensor for a solid sphere of radius $R$. I have done this and found it to be $$\frac{2}{5}MR^2 \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}$$ I'm now asked to find the inertia tensor for a…
MHW
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Constant angular acceleration

An object with known initial orientation and angular velocity $\omega_0$ is subjected to constant angular acceleration $\alpha$. Its final orientation at time $t$ is some rotation of its initial orientation. How can I find this rotation? Angular…
SteveB
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How to calculate this particle's position, velocity and acceleration, each as functions of time.

I'm given a particle of mass $m$, at position $x$, moving through 1-space dimenion with velocity $v=\gamma(d-x)$ for constant $\gamma, d.$ I'm also given that the particle starts from $x=0$ at $t=0$. My question is: how do I find the velocity (and…
beep-boop
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Question Concerning Terminal Velocity

Question: A ball of mass m is thrown vertically upward with initial velocity $v_0$. Air resistance is proportional to the square of the velocity. If the terminal velocity of the ball is $v_t$, show that when the ball returns to its original position…
Vladimir Nabokov
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Bead on rotating wire - differential equation

Consider a bead sliding on smooth straight wire. Wire is rotating in vertical plane with constant angular velocity. Gravitational force is vertically downward as usual. Equation of motion of the bead is: $$ m\ddot r = m\omega^2r - mg\sin(\omega t),…
atom
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Equation of motion Pendulum using $w=e^{ix}$

I'm working with the equation of motion for a pendulum as follows: $$x''+ \frac{g}{l} \sin (x)=0$$ Where $x$ is the angle between the pendulum and the vertical rest position. I am required to use the complex variable $w=e^{ix}$ to rewrite the…
Moira
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Mechanics exercise using Newton’s second law.

Could anyone help me with this question?- Suppose a particle of mass m with position $x>0$ moves in 1D space under the influence of the gravitational force of another point particle with mass $M$ sitting at $x=0$. The question gives $$\mathbf…
Gracie
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