Classical mechanics refers to the classical (i.e., non-relativistic, non-quantum) study of physics. Three major formulations of classical mechanics are newtonian mechanics, lagrangian mechanics, and hamiltonian mechanics. The latter two are rather useful in extensions to Classical Mechanics; ...

learn more… | top users | synonyms (1)

1
vote
3answers
545 views

Advantages/Disadvantages of “hanging off” a motorcycle when leaning

The closest question I could find with regards to this subject was this one: Countersteering a motorcycle However, it does not address the specific physics of what I would like to know. There are 3 ...
1
vote
1answer
127 views

When does a Trebuchet Shoot Its Projectile?

Consider the following sling trebuchet: While researching I found that what controls the release angle of the projectile is the angle between the 'finger' and the extension of the beam $r_b$, as ...
1
vote
1answer
76 views

Understanding Newton's Laws of Motion

I'm having difficulty understand Newton's laws of motion in practice, and how to model true dynamic systems. There are two examples below, where I cannot quite figure out what the true forces and ...
13
votes
9answers
7k views

What is the difference between translation and rotation?

What is the difference between translation and rotation ? If this were a mathematics site, the question would be at best naive. But this is physics site, and the question must be interpreted as a ...
0
votes
0answers
57 views

Acclerated Coordinate Systems: Motion on the surface of the Earth (Fetter and Walecka)

So I am STRUGGLING, absolutely STRUGGLING to understand an example in my textbook. That's how bad I am, I can't even figure out how to do the example in my textbook. Anyway, I'm reading "Theoretical ...
2
votes
1answer
76 views

Relationship between zero modes and symmetry in a simple system of coupled springs

This Wikipedia page states that "zero modes appear whenever a physical system possesses a certain symmetry," and gives the example of a ring of beads connected by springs having a zero mode associated ...
1
vote
0answers
42 views

Reason behind $L = T - V$ (Lagrangian formalism) [duplicate]

I've been learning about the Lagrangian formulation recently, and while I'm with the process, I am still struggling somewhat with the theory behind it. As I (rather poorly) understand it, the ...
16
votes
3answers
416 views

Momentum of transverse waves on a string

In general, if a wave carries energy density $u$ with velocity $v$, it also carries momentum density $u/v$. I've seen this explicitly shown for electromagnetic waves and (longitudinal) sound waves. ...
1
vote
1answer
49 views

Lagrangian in a system with a specific velocity dependent potential

I have a system of a particle moving under the generalized central potential $$ V= \frac{1}{r}(1+\dot{r}^2) \tag{1} $$ The general Euler-Lagrange equations for such type of potentials are: $$ \frac{...
2
votes
2answers
79 views

Difference between naive and Coriolis-force calculation

Consider the classical problem of dropping a coin from a tower at the equator of a planet without atmosphere and with spin $\Omega$: where in relation to a plumb-line will the coin land? When doing ...
6
votes
1answer
83 views

How does a lever magnify force? [duplicate]

I understand that energy is conserved when a force is applied to the end of a lever and magnified closer to the pivot point. However, I would like to know how it is the force is transferred and ...
1
vote
2answers
67 views

Tractrix - velocity pointing to pulling point

It is said the tractrix is the curve described by a mass being pulled by a string, where the end of the string being pulled moves with constant speed, and the mass suffers a friction force. What is ...
1
vote
1answer
37 views

Homework exercise: a ball hits a rigid bar [closed]

I need a hand with the following exercise: A rigid bar of mass $M$ and length $L$ is hanging vertically from it's upper side, from which it can rotate freely. A particle of mass $m$ hits the ...
5
votes
8answers
3k views

Can we explain Newton's first law mathematically?

At constant speed there is no acceleration. $(f'(x)=v'=0=a)$ .If $a=0$ then $F=ma=0$ and therefore no force acts on the object so the object will continue in the same direction, if any. This is only ...
0
votes
0answers
28 views

Elastic Deformation coupled to simple oscillator

I have a system which I'm attempting to model as a spherical mass on a spring (cantilever) from above, and a somewhat elastic surface below. Are there any resources on how to model the resulting ...
0
votes
2answers
58 views

Rotating Frames of Reference: Doubt while deriving the velocity

I am following an online Chapter on Coriolis force, where the author develops the equations for a rotating frame of reference. The Figure and most of the notation used in the derivation can be ...
1
vote
1answer
50 views

Stability of the classical helium atom

Let us forget about quantum mechanics and confine ourselves to classical mechanics. The Hamiltonian for a classical helium atom would be $$ H = \frac{p_1^2 + p_2^2}{2m } - \frac{Z}{r_1} - \frac{Z}{...
0
votes
1answer
81 views

Solving 9 variable Normal Reaction equations of Sudoku board [closed]

We have a rigid Square board of negligible mass, which has been divided into a grid of 9 small squares(like a Sudoku Board), at centre of each square a point mass is attached. The gravity on the board ...
1
vote
1answer
72 views

Hamiltonian flow?

I was wondering what the Hamiltonian flow actually is? Here is my idea, I just wanted to know if I am correct about this. So let $(x(t),p(t))' = X_{H}(x(t),p(t))$ are the Hamilton's equations and $...
1
vote
2answers
147 views

What is the inconsistency between Maxwell's electrodynamics and newtonian mechanics?

As far as I understand, when a modification of a theory is made it is because some observation required this modifcation. Quantum Mechanics is a nice example of that: observations of microscopic ...
3
votes
3answers
166 views

Mathematical Formulation of Classical Spacetime

I have seen two formulations of Classical Mechanics: Newtonian spacetime (learned it from the lectures of Professor Frederic P. Schuller): Definition: A Newtonian spacetime is a quintuple $(M, \...
7
votes
1answer
139 views

How to properly use Perturbation Theory in classical systems?

Context: If we consider a particle in upwards motion near the Earth's surface and acted by a quadratic drag we get the non-linear eom: $$\frac{dv}{dt}=-g-\frac{b}{m}v^2.$$ We can solve it ...
2
votes
2answers
109 views

Validity of the Lyapunov exponent approximation

I was trying to get the Lyapunov exponent for some dynamical nonlinear systems and found that it is not true (as I had expected) that the distance between two trajectories with slightly different ...
1
vote
1answer
57 views

Classical dynamics of a matrix

For a system of interacting particles, we can formulate Hamiltonian dynamics in terms of a vector of position coordinates $q$ and a vector of momentum coordinates $p$. Then the Hamiltonian takes the ...
1
vote
1answer
58 views

Why does time-independent Hamiltonian not depend on angle variable?

In Landau and Lifshitz Mechanics, $\S50$ Canonical variables a time-independent Hamiltonian is considered, and a canonical transformation is done such that adiabatic invariant $I$ becomes the new ...
0
votes
2answers
187 views

Infinite pulley system

http://www.physics.harvard.edu/uploads/files/undergrad/probweek/sol43.pdf Hi, I've been trying to solve this question for a while, I understand the first solution and also the solution to the second ...
0
votes
1answer
75 views

Springs, elastic potential energy, kinetic energy

If a ball with some kinetic energy collides with a spring, the ball doesn't lose its kinetic energy in an instant, right? it loses kinetic energy as the spring gains potential elastic energy. Right? ...
1
vote
0answers
26 views

The geometrical-locus result of collision and fall

A classical momentum-conservation experiment follows about this way: On a table there is a sloped track and a ball is rolled down. At the bottom of the track, a second ball is at rest. The balls ...
1
vote
2answers
53 views

How do I find the linear components of acceleration in a pendulum?

I have managed to derive the equation of motion of a simple pendulum under the influence of gravity using the Lagrangian, but since that only tells me what the angular acceleration is, I now want to ...
-1
votes
1answer
65 views

Why is angular acceleration of a pendulum always negative?

I was trying to derive using the Lagrangian the equations of motion of a simple pendulum under the influence of gravity. Eventually, I was brought to this conclusion: $$\alpha = -(g\sinθ)/l$$ where $\...
2
votes
1answer
342 views

Hyper/parabolic kepler orbits and “mean anomaly”

In an elliptical kepler orbit there is an easy recipe to describe the motion/position of a satellite at time $t$. One just follows the following steps - an important detail for me is that the ...
8
votes
4answers
793 views

Does Dirac's argument against classical mechanics stand in contradiction to Bohm's theory?

In his book on Quantum Mechanics, P.A.M. Dirac talks about the stability of the atom as a means of demonstrating the need for quantum mechanics. He writes: The necessity for a departure from ...
3
votes
2answers
4k views

degree of freedom of a rigid body 5 or 6?

I'm confused here. I have a three particle (rigid) system. What would be the degree of freedom? I found out five. 3 coordinates for center of mass and 2 for describing orientation. But we have only ...
-1
votes
1answer
51 views

Why can't you ride a bike with a fixed handlebar?

I tried one time, as part of an experiment, to ride a bike with a fixed handle bar. Impossible. So, in any case, our movements made with the handlebar helps us in not falling down. I can feel kinda ...
1
vote
1answer
40 views

Why surface tension behaves so differently?

When a needle (or any other object) floats on water, its acting upwards balancing the gravity. But when an object (or may be a needle suspended in water) submerged in water, it acts downwards. ...
0
votes
0answers
12 views

Piezoelectric slab (cantilever) with voltage

I am studying this specific piezoelectric slab with voltage applied The piezoelectric equation is $$ \left[ \begin{array}{c} \sigma_{1}\\ \sigma_{2}\\ \sigma_{3}\\ \sigma_{4}\\ \sigma_{5}\\ \sigma_{...
0
votes
1answer
35 views

How does string tension influence the harmonic spectrum?

Hey there fellow physicists & musicians! I have a question both physics and music related. How does the string tension affect the sound spectrum? More precisely, how do the respective ...
0
votes
1answer
59 views

Velocity from the cumulative distribution function of the Boltzmann distribution

I want to get a Boltzmann distribution of the $v_x$, $v_y$ and $v_z$ velocity components (please, notice that the distribution is one-dimensional). To do so, I need the cumulative distribution ...
0
votes
2answers
41 views

Galilean invariance and the Lagrangian

My textbook says that in a time invariant space with translational and rotational symmetry the Lagrangian only depends on the magnitude of the velocity. The galilean invariance says that a Lagrangian ...
-1
votes
1answer
56 views

Force and energy relation: in case of time dependent force

The equivalent problems are also found in Marion problem 7-22, and other formal classical mechanics textbook. Here what i want to know why instructor solution and some websites gives this kinds of ...
1
vote
0answers
62 views

Which condition is stronger - ergodicity or mixing?

Reading a statistical physics book, I've encountered the following assertion (without further explanations): [..] the presence of dynamical instability makes the trajectory of a system much more ...
3
votes
1answer
44 views

Problem books for concept building in applications of Riemannian and other geometries to mechanics

As a student of physics I have learned solving Euler equations for rigid bodies by solving examples and exercises in self-contained books rather than understanding the proofs of Euler equations (I ...
1
vote
1answer
34 views

Finding the Mass of a Precessing Top

Consider a symmetric, non-nutating precessing top with one point fixed (the tip if you will). It's symmetry axis is at an angle $\theta$ to the vertical and it steadily precesses at some angular ...
4
votes
1answer
70 views

What is the specific source(s) of sliding kinetic friction

In simplistic (K-8) physics classes, it seems to be generally instructed that the friction between two moving surfaces is due to the unevenness of each surface and the microscopic roughness. However, ...
25
votes
4answers
1k views

Does topology have any role in classical physics?

I've seen many applications of topology in Quantum Mechanics (topological insulators, quantum Hall effects, TQFT, etc.) Does any of these phenomena have anything in common? Is there any intuitive ...
0
votes
2answers
76 views

Average acceleration: why I am getting different results?

Let's consider a simple school problem. A car starts moving during 3 seconds with a constant acceleration of 1 m/s^2. Then it stops accelerating and moves 3 seconds more with a constant speed. Find ...
-3
votes
1answer
64 views

What happens to gravitational potential when the mass disappears?

This is from a section of my website. Please tell me where it is wrong. Consider two stationary gaseous planets, both made entirely of deutrium. As the two planets are moved closer to each other ...
2
votes
2answers
349 views

Clearing up confusion about calculating torque

Suppose you have a shape consisting of two perpendicular rods (the whole shape is a rigid body) which stands upright so the plane of the rods is perpendicular to the plane of the ground, and the ...
3
votes
1answer
56 views

Why does the 'Jacobian of at least one combination of $n$ functions shall be different from zero'?

I've started reading The Variational Principles of Mechanics by Cornelius Lanczos; here is the concerned excerpt from p. 11: The generalized coordinates $q_1,q_2,\ldots, q_n$ may or may not have a ...
3
votes
1answer
53 views

A pendulum attached to a spring and all the system is rotating with angular velocity

Find the all the constraints and a set of generalized coordinates A pendulum attached to a spring and all the system is rotating with angular velocity $\omega$. this is what I have done, I do not ...