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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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22 views

Forced oscillating spring-mass system terms

I have an equation, and I want to know the physical significance of each of the following terms: $E(t) = E(0) + \int_0^t g(s)u'(s)ds -\gamma\int_0^t[u'(s)]^2ds$ where $g = mu'' + \gamma u' + ku$. I ...
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1answer
21 views

To find the acceleration of three blocks and the tension of strings if they are horizontally placed and pulled from the Right side

Find the Acceleration of blocks A, B and C, and tensions in the strings. All the blocks are of equal masses of 10kg. Also F = 60N. Let's name the leftmost block as A, middle one as B and Rightmost ...
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3answers
55 views

Wave and relativity

From Wikipedia, "In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport." But Einstein said that energy equals mass so if a wave ...
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0answers
40 views

Mathematical Prerequisites for Classical Mechanics by V.I. Arnold [on hold]

Could someone please tell me the mathematical pre-requisites for Arnold's Classical mechanics book. This is specifically to understand statements like "Affine n-dimensional space An is ...
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2answers
38 views

Can average acceleration be exactly determined from discrete points separated by equal time intervals?

I believe the answer is no. But I want to be sure. The objective is to determine an exact value for the average acceleration of a projectile moving in a plane. The given data consists of a series ...
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1answer
25 views

Amplifying stress at near perfect vacuum?

So, I've got a vacuum chamber as part of a home freeze drying project. It is a cylindrical steel pot with a 1.5in acrylic lid. The manual is poorly translated from Chinese, so some of it is seemingly ...
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1answer
40 views

Analytic and numerical integration of the rocket equation yield different results [on hold]

Background The mass of a rocket as a function of time is: $$ m = m_0 - \dot m t$$ Where $m_0 $ is the initial mass of the rocket and $\dot m$ is the mass flow rate. At a certain time all the fuel has ...
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0answers
40 views

Newtons second law appliance [on hold]

Assume we have one box, and we put another box on it. A box of $m_1=4\ \rm{kg}$ and a box of $m_2=2\ \rm{kg}$. The box with more mass ($m_1$) is in the bottom. What will happen if we apply a force of ...
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1answer
58 views

Lagrange Equation - Basics

The basic equation of Lagrange is given by, $$\frac{\mathrm d}{\mathrm dt} \frac{\partial L}{\partial \dot{q_j}} - \frac{\partial L}{\partial q_j} = Q_j \tag{1}$$ where $T$ is the kinetic energy, $V$ ...
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0answers
14 views

Cauchy problem for Hamilton-Jacobi equation

In Arnol'd V.I, "Mathematical methods of classical mechanics" p.257, I was asked to find a solution for the Cauchy problem $$H=\frac{p^2}{2},\ \ \ S_0=\frac{q^2}{2}$$ of the Hamilton-Jacobi equation ...
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0answers
11 views

Center of Buoyancy of changing displacement water [on hold]

how do I calculate the center of buoyancy of changing displacement of water?
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2answers
28 views

Work done to change circular orbit and orbital speed

If a satellite of mass $m$ is orbiting a planet of mass $M$ with radius $r_1$ and orbital speed $v_1$ and is brought to orbit at $r_2$ with speed $v_2$, its kinetic energy changes by a quantity $$ \...
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0answers
15 views

Do Newton's laws imply independence of generalised coordinates and generalised velocity? [duplicate]

When deriving lagrangian formulation from Newton's laws, We use the fact that generalized velocity and generalized coordinates are independent of each other. Is there a mathematically rigorous proof ...
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0answers
18 views

Conservation of momentum and energy question [on hold]

A small wooden block with mass 0.800 kg is suspended from the lower end of a light cord that is 1.60 m long. The block is initially at rest. A bullet with mass 12.0 g is fired at the block with a ...
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1answer
89 views

Silly question about kinematics and Christoffel symbols

An interresting "method" that allows you to know the acceleration vector with respect to any coordinate system is just a matter of recognize some key formulas. 1) Given the metric of a particlar line ...
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0answers
78 views

Solve equations of motion to find $\Phi(t)$ for a pendulum with an infinite period

Consider a pendulum of mass $m$ and length $l$ that can rotate in the vertical plane subject to the gravitational field $g$. Write down the Lagrangian and solve the resulting equation of ...
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0answers
30 views

Can we create completely vacuum box? [on hold]

Can we create completely perfect vacuum? Is there any theoretical problem for this? Not technological, but theoretical?
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0answers
24 views

A point charge on the perfect conductor and effective potential [on hold]

A perfect conductor is filling the region $x<0$ of space, and a uniform magnetic field $B>0$ is applied along the $z$ direction. A particle with mass m and electric charge $q>0$ is placed at $...
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0answers
40 views

On the performance of Bolt in the 100 metre sprint - solving equation of motion [on hold]

I'm looking at the following article(1) in which a mathematical model is used to describe the performance of Bolt (in general of a sprinter) in a 100 m sprint. The equation of motion is $$ m\dot u = ...
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1answer
26 views

Relationship between strain energy function and strain or stress

How one can get the strain or stress from the strain energy function ? And if one cannot do it, what is the use of that function ?
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2answers
29 views

Problem on deriving canonical transformation condition

I'm trying to compute how a canonical transformation should be, given that preserve the symplectic form and trying to recover the condition on the Poisson Bracket. I then start with $$\omega=\stackrel{...
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0answers
12 views

max deflection of a cantilever beam of two different material [on hold]

How to calculate the maximum deflection of a cantilever beam of two different material stacked lengthwise as shown in the figure. The load is point load. How to approach such a problem? Thank you.
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0answers
16 views

Equation of motion for double pendulum [closed]

I have derived the Lagrangian of a double pendulum considering the pivot point of the first pendulum is the origin. Am I correctly derived the Lagrangian?
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1answer
39 views

Rotation with Zero Angular Momentum [on hold]

I'm working on a problem that I think I solved but I'm suspicious of my solution. We've got a massless disk of radius 3, with 4 point masses as shown in the image. The masses rotation about $x=\pm 2$ ...
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0answers
30 views

Hamilton-Jacobi theory vs Hamiltonian formalism

I'm writing some notes on Hamilton-Jacobi Theory and I'd like to find an example of a system that is quite difficult to integrate in the usual Hamiltonian formalism, but quite easy in the Hamilton-...
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0answers
33 views

Newton versus Huygens

I have heard that Huygens also gave a foundation to classical mechanics that is equivalent to Newton's. What is the difference between their approaches?
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0answers
27 views

Astronaut auto-propulsion [closed]

Imagine, if you will, a space station. Within, it's crew. Imagine further, that one of the crew has fallen afoul of their crew mates. Their singular eating habits have caused considerable hostility, ...
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2answers
53 views

Pendulum with rope vs. rod

We know that when a pendulum with a rope is at its maximum height, there is no tension in the rope and no force on the pivot. If we consider the same situation and position, but where the rope is ...
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0answers
55 views

How to start understanding physics in depth from the basics? [closed]

I am a first-year Computer Science Engineering student, and I want to work on the engineering end of the spectrum in the future. My high school physics teacher really sucked. I will have my physics-...
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0answers
53 views

Goldstein central force problem [closed]

I was reading Goldstein chapter 3 central force motion. I tried to do the exercise 21 on p. 130 of 3rd ed. but cant think of any way how to do it. any clue would be very helpful. Show that the ...
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0answers
30 views

Partial derivative in generalized coordinates [duplicate]

Sorry for my broken English. I'm a physics undergrad and quite poor at math. I just started to learn analytical mechanics and it really confuses me. my analytical textbook uses the equations below ...
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1answer
26 views

If every object could give an equal and opposite force to what we apply then why do the objects exhibit translatory and rotational motion? [duplicate]

If I push a block on a frictionless surface with enough force, it begins to move. Shouldn't it be standing still if it exerts an equal force on me as per 3rd law?
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1answer
54 views

Do group elements correspond to observables of a system, or to transformations of a system?

Most groups I encountered so far in classical mechanics an special relativity (Galilei-group, Poincare-group, Lorentz-group and so on) described transformations of the system that was to look at. This ...
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0answers
47 views

Why do i get the wrong answer when i try to solve for Vf if I use The Conservation of Momentum instead of The Conservation of Kinetic Energy? [closed]

I apologize if this question has been asked before but I am having a very difficult time understanding why we must use The Conservation of K.E. instead of The Conservation of Momentum. Thank you]1
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0answers
18 views

Deriving gyroscope basic equation from Lagrangian formalism [duplicate]

The following represents the equation of motion of a gyroscope: $$ \frac{d\vec{L}}{dt} = \vec{r} \times m\vec{g} $$ where $\vec{L}$ is the gyroscope's angular momentum, $\vec{r}$ is the vector ...
2
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1answer
33 views

Why does a constant force on a rigid body with a fixed axis of rotation produce more angular acceleration if applied farther from the axis?

I know the eq torque = Ia and also torque = Fr... it's easy to see mathematically but not physically. I want a simple physical justification for it.(may be microscopically).
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2answers
51 views

Must the varied paths in the action be physically possible?

For simplicity without loss of generalization, consider a free particle. When using the Principle of Least Action, I imagine all variations of the true path between $t_1, t_2$ regardless of whether ...
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0answers
31 views

Question on hard spheres collision

My question is very simple: is it true that if I have a collision of two hard spheres, then the vectore of change of the momentum lies on the line connecting the two centers? Thank you!
2
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1answer
70 views

Is *every* planar/2D system integrable?

Consider the generic following planar/2D system: $$\begin{cases} \frac{dx}{dt} = A(x,y)\\ \\ \frac{dy}{dt} = B(x,y), \end{cases}$$ where $A,B$ are two functions. Reading Classical Mechanics by ...
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2answers
38 views

Is the direction of average velocity the same as that of average acceleration and that of displacement?

Average velocity is defined as: $\vec{\Delta v} = \frac{\vec{\Delta r}}{\Delta t}$, and average acceleration as $\vec{\Delta a} = \frac{\vec{\Delta v}}{\Delta t}$. It is apparant from these ...
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0answers
36 views

Toughness of material to be not damaged by impact / penetration [closed]

A bullet has mass $m = 0.2 \; \text{kg}$ and speed $v = 700 \; \text{m/s}$. The tip of this bullet is a circle with $S = 1 \; \text{mm}^2$. Now this bullets hits a target which is made from some ...
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0answers
45 views

What about objects' properties in physics?

Some scholars talk about propensities or dispositions when they refer to some non-manifest properties of entities. I.e. The property of being soluble is a non-manifest one because only if sugar is put ...
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0answers
36 views

What does it mean for a force to 'produce' virtual displacement?

Book: Variational Principles of Mechanics by Lanczos (page 80) Statement: "Two systems of forces which produce virtual displacements are dynamically equivalent." I don't understand the part about ...
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1answer
38 views

Force input to harmonic oscillator force as function of time or displacement as function of time? [closed]

Question title basically says it. If the governing equations are like: $$x''m_1 = c({x_1}'-{x_2}') + k_1({x_1}'-{x_2}') = f(t)$$ etc... Since all the terms are force terms, shouldn't the input ...
3
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1answer
48 views

Application of Darboux's theorem to magnetic field line flows

In this famous paper by Cary and Littlejohn on noncanonical Hamiltonian mechanics and its application to magnetic field line flow, they claim that as a result of Darboux's theorem, it is always ...
3
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1answer
69 views

Boundary conditions for calculus of variations in phase space and under canonical transformations

This might be a stupid question, but I just don't get it. In Hamiltonian mechanics when examining conditions for a $(\boldsymbol{q},\boldsymbol{p})\rightarrow(\boldsymbol{Q},\boldsymbol{P})$ ...
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1answer
37 views

Angular velocity by velocities of 3 particles of the solid

Velocities of 3 particles of the solid, which don't lie on a single straight line, $V_1, V_2, V_3$ are given (as vector-functions). Radius-vectors $r_1, r_2$ from third particle to first and second ...
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0answers
14 views

Can a car accelerate on a frictionless surface? [duplicate]

i have string of related questions. i know that the internal forces cannot result in acceleration of a body and so in daily life, car engine applies force to rotate wheels that produce friction force (...
2
votes
1answer
66 views

Schwinger's variation of the action of point particle with *both* time and position as independent variables

In Chapter 8, pages 86-87, equations (8.5)-(8.11) of Julian Schwinger et al., Classical Electrodynamics, the equations of motion for the following action principle of a point particle in an external ...
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0answers
32 views

Lagrangian perturbation theory

I have a system of coupled non-linear differential equations which stem from a Lagrangian and the Euler-Lagrange Equations. I want to solve them with perturbation theory. I know that in Quantum ...