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Questions tagged [classical-mechanics]

Classical mechanics discusses the behaviour of macroscopic bodies under the influence of forces (without necessarily specifying the origin of these forces). If it's possible, USE MORE SPECIFIC TAGS like [newtonian-mechanics], [lagrangian-formalism], and [hamiltonian-formalism].

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26 views

Transformation between a dynamical system to a Hamiltonian system [duplicate]

Consider a dynamical system characterized by these equations $$\dot{x}=x-xy \\ \dot{y}=-y+xy$$ If we transform $\ln(y)=q$ and $\ln(x)=p$, the system can be changed into a Hamiltonian system with $q$ ...
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Phenomenon: dust in candle wax

I happened to encounter an interesting phenomenon in candle wax. As shown in the video, small dust near the fire seem to move back and forth, as if there is some kind of repulsive and attractive ...
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Lagrangian Involving a Integral

This is my first post here, so do let me know if I am asking anything or in any manner unproperly! I am trying to construct a Lagrangian for a dynamic Euler-Bernoulli beam (with one end cramped) with ...
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1answer
23 views

Conservation of Angular Momentum On Applying an Impulse

If a rod of length l is placed on a frictionless horizontal surface and an impulse P is applied along the plane of the horizontal surface on the rod at a point O which is at a distance d (d≠0) from ...
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Inconsistency in the expression for $d\alpha= d\alpha_k \wedge d\xi^k$ contracted with pairs of vector fields

Classical Dynamics: A Contemporary Approach, Jorge v. Jose and Eugene J. Saletan,(1998) states in page 227 that Globally $d\alpha$ is defined by its contraction with pairs of vector fields: $$...
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Normal force per unit lenght that the string applies to the disk

I read D.Morin Classical Mechanics Problem book. The following from his book from 2.chapter 2.6 problem: Problem: Find the Normal force per unit lenght that the applies to the disk. In solution he ...
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2answers
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Why does the scattering cross section equal to the sum over all differential cross section; including the incident angle?

According to Beer Lambert's law, the intensity of light passing through a homogeneous medium diminishes at a rate proportional to the incident intensity; i.e. $$ \frac{dI(s)}{ds} = -I(s)\sigma\, , $$ ...
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How can I calculate the pressure at every point under a block, which rests on a slope?

A cubic block with uniform density $\rho$ and side length $a$ rests on a slope, with one of its face facing directly downwards. The slop is inclined at an angle $\theta$ with the horizontal. Assume ...
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How can the acceleration of a person on a zipline be calculated?

I was thinking one day about how a speed, or perhaps the acceleration, of a person riding a zip line could be calculated. I first started by thinking of an ellipse where the two foci were the anchors ...
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Write Equations of motion and a phase portrait of a point particle [on hold]

A point particle with mass m = 1 moves along the X axis under the the force $f (x) = x^3 + x^4$. Write the equation of motion of the point and draw a phase portrait. What I have so far: So, $f = m\...
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1answer
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Write Equations of motion of a point particle that moves on the surface of a paraboloid [on hold]

I'm not a physics major student and I call myself a total noob in physics, however, I have this issue to solve. The problem is that I don't even know where to start from. One little thing to add: this ...
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2answers
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Would a speed camera register more speed if it moves in the opposite direction than the object it's measuring?

Earlier today, I was talking with my friend about speed cameras measuring different speeds when moving. This is the situation: I am the red car and I'm driving ...
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1answer
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Why reduced mass in Central force field moving under the action of internal force?

I did the derivation of equivalent one body problem where we get, $$\mu\frac{\text{d}^2r}{\text{d}t^2} = F_{\text{internal}}$$ But I don't understand even when internal force between two bodies are ...
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Time derivative of classical position and momentum averages

Consider a one-dimensional Hamiltonian system $H(q,p,t)$, and some classical phase space distribution function $\rho(q,p,t)$ satisfying Liouville's equation $$\frac{\partial \rho}{\partial t} = \{H,\...
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1answer
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Calculate new hight of a moving object being hit from underneath [on hold]

I have an old exam-question I have truoble understanding. A skeet with mass M = 0.25 kg is fired away with initial speed 25 m/s and 28 degrees. When the skeet has ...
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1answer
26 views

Reynold's Transport Theorem explanation [on hold]

Can anyone help me to understand the passages in this theorem, I'm trying to resolve it but it's blowing my mind
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42 views

Lagrangian and Hamiltonian formulations [closed]

Which is the best way to learn the formulations of classical mechanics after a course in classical and relativistic Dynamics?
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Molecular dynamics - Fermi Pasta Ulam Tsingou

I'm taking a course on computational physics, but still fairly new to physics at this level, and because of that, I'm looking for some help getting a better understanding of the following. Working on ...
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0answers
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Is the incompressibility the only condition I could use for this problem? [closed]

The problem is In cylindrical coordinates, the velocity is $\mathbf{u}=u_{r} \hat{\mathbf{e}}_{r}+u_{\theta} \hat{\mathbf{e}}_{\theta}+u_{z} \hat{\mathbf{e}}_{z}$. Conside an incompressible flow ...
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1answer
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Force Applied but No Distance Travelled

Suppose I push on a wall with a constant force of 5 N for 10 s. The wall won't move and hence no work will be done on the wall. However, pushing requires energy. How can I find out how much energy I ...
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Uniform circular motion /centripetal motion [closed]

A particle starts moving along a circle of radius (40/π) m with a constant tangential acceleration. If the velocity of the particle is 120 m/S at the end of the second revolution after the motion has ...
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1answer
21 views

The velocity of an object leaving the inclined plane

I saw the question below in our physics textbook. It asks A block of mass m is released and slides down on the frictionless inclined surface ( the inclined plane is of concrete and doesn't ...
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2answers
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What are two different angles we can throw a ball, so it lands at the same spot? [closed]

This is not a particularly difficult task, but it has given me a lot of trouble and I can't solve it. We throw a ball at 60° angle with a speed of 20 m/s. The ball lands 35.2 m away. What is the ...
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3answers
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Do proteins interact through classical or quantum mechanics?

For the protein interactions that occur in our cells, do they "follow" classical mechanics or quantum mechanics when interacting? I have zero knowledge about quantum mechanics, but I was wondering ...
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2answers
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Can we detect a cyclic coordinate by just inspecting the Lagrangian?

I'm reading through Susskind-Hrabovsky's Theoretical Minimum. On page 126, where they are talking about cyclic coordinates, an example is given: Suppose two particles moving on a line with a ...
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2answers
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On source of heat energy dissipation in a system

Suppose we have a block of mass m which was at rest on a rough floor and is now given an impulse towards a wall.It is given that the collision with wall is perfectly elastic and no energy is lost in ...
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If the lagrangian density changes by a total derivative of the lagrangian density

When we derive energy momentum tensor current by actively transforming field. We see that lagrangian ( density) changes by a total derivative of the lagrangian. If a total derivative of the function ...
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3answers
148 views

Inconsistency of PE to KE conversion in moving reference frames

Here's a nice trick question to keep you amused over the weekend. A trolley of unit mass with light frictionless wheels is released to roll down a ramp onto a smooth level surface. The PE lost equals ...
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37 views

Derivation of the time-derivative in a rotating frame of refrence

I have so trouble following Goldsteins derivation of the time derivative in the rotating refrence frame, and its use to derive the coriolis force (sec. 4.9-10) Given an intertial frame of refrence, $S$...
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Classifying all symmetries of a mechanical system [duplicate]

Given a newtonian mechincal system with $n$ objects, we may think of it as living in $\mathbb{R}^{6n+1}$ ; one dimension is time, $3n$ dimensions for velocities, and $3n$ for positions. We then have ...
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Physics Simulation of a Simple Pendulum with Drag Forces

I am working on simulating a simple pendulum with present drag forces. My task is to use numerical methods (I am using Verlet integrator) to estimate the angle as a function of time, as well as the ...
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Euler's Equation of Motion by Lagrange's Equations [duplicate]

currently i am studying three dimensional rigid body dynamics. My question is how to derrive the popular Euler's Equation of motion given by: $\sum M_x = J_x\dot{w}_x-(J_z-J_y)\omega_y \omega_z $ $\...
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1answer
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Which of these would be the same for both objects? [on hold]

Two balls are dropped from the same height at the same instant. At any moment, what will be the same for both? A. Total velocity B. Height C. Momentum This is a conceptual question, so I don't know ...
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1answer
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Can I 'add potential together'?

I have the Lagrangian function for a particle in an electromagnetic field $$L = \frac{1}{2} m \dot{\mathbf{r}}^2 + q \dot{\mathbf{r}} \cdot \mathbf{A} (\mathbf{r}, t) - q \phi (\mathbf{r}, t)$$ If I ...
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1answer
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Even and odd polar coordinates in general orbits

I'm learning about orbits in classical mechanics at the moment. I'm not understanding something about the evenness of the distance component and oddness of the angle component. I see that the radial ...
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1answer
34 views

When can you simplify partition function and Hamiltonian for a classical fluid?

I am new to statistical mechanics and classical mechanics. A set of $N$ classical particles has a Hamiltonian \begin{equation} \mathcal{H} = K_N(q^{3N},p^{3N}) + U_N(q^{3N},p^{3N}) \end{equation} ...
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What is the intuitivity about C*-Algebras being used as the fundamental objects in physics?

While asking about operators on this site, many answers mentioned "C*-algebras" to be the fundamental mathematical element corresponding to an observable (in QFT and QM at least), and choosing a ...
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2answers
36 views

Conservation of total energy for a system with holonomic constraints

Consider a system with generalized coordinates $u_1, u_2$ and $u_3$ such that $u_1$ and $u_2$ are dependent through the following holonomic constraint \begin{equation} G(u_1, u_2)=0. \end{equation} It ...
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1answer
78 views

Rotational motion integration (Rigid body dynamics)

I am trying to integrate the rotational motion of a rigid body (a set of N point masses) $\textbf{in the inertial frame}$, but my results seem totally wrong. What of the following steps could be wrong?...
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1answer
32 views

Rotation of top of symmetries

while learning about rotation, I started to wonder what forces will come into play. Lets picture a top with two masses centered at (-1,0,-1) and (1,0,1) with rods connecting the masses directly to the ...
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Effect of external forces on a horizontal mass dampener

I am reading this paper which models the motion of a horizontal mass dampener. They say that on adding a dampener, the equation consisting of the forces is: $ma = -cv -kx$ where $ c$ = damping ...
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Does a static-firing rocket engine do work?

Is the "working fluid" doing any work during a static-fire of a rocket engine. Since the rocket is held stationary, there is no work being done on the rocket right? However, is the exhaust doing work ...
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1answer
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Inserting Wind effects on a rocket trajectory simulator

I`m more used to the math.stackexchange so i really don't know how much information about my problem i should provide, if it is not enough i'll add more. So, basically i already have a 6DOF ...
0
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1answer
86 views

Calculation of final temperature [closed]

what would be the final temperature of any body with the change in the ambient temperature? A Body temperature was recorded at 27.2°C ambient temperature is 60.2°C Final temperature of body is 60....
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Advantage of narrow cords in bifilar pendulums

I'm a high school student doing further reading for a project I'm starting and I came across this experiment. On slide eight it mentions that the fibres holding up the pendulum are 0.2 mm in ...
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1answer
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Covariance of the perfect fluid's stress tensor

In Special Relativity, for a perfect fluid (i.e. without heat transference or viscosity) we have a stress tensor $T_{\mu \nu}$ $$ T_{\mu \nu} = -p\eta_{\mu \nu} + (\rho + p)u_\mu u_\nu $$ It is said ...
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Is there a mechanical system with potential $V(\theta) = a \cosh(\theta)$?

The potential of a pendulum reads $$ V(\theta) = mgl(1-\cos(\theta)) \, .$$ Is there any similarly simple system with potential $$ V(\theta) = a \cosh(\theta) \, ,$$ where $a$ is some constant that ...
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0answers
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Deriving the dynamic friction of an oversize shaft in a hole

I want to derive the force of dynamic friction of an oversized shaft in a hole. Suppose the dynamic coefficient of friction is $\mu$. Here is my attempt. Suppose the hole has diameter $d$ and the ...
3
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1answer
40 views

Intermediate axis theorem in higher dimensions

The intermediate axis theorem states that the rotation of an object around its first and third principal axes is stable, while rotation around its second principal axis (or intermediate axis) is not. ...
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1answer
34 views

Damped Oscillation and Period

In my school experiment, I wanted to measure the gravitational constant ($9.81 \ m/s^2$) by using a pendulum. If we take into account the damped oscillation (i.e. friction forces), does that affect ...