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; ...

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What justification is necessary for convolutional variational principles to be considered legitimate?

I recently asked a related question and was interested in why/or why we cannot use convolutional variational principles in practice or in theory. Summarizing the points I made in the earlier post: ...
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1answer
40 views

Can individual forces be regarded as momentum flows? [on hold]

Net force on an object can be defined in two ways equivalently (from a classical point of view): $$\vec{F} = m\frac{d\vec{v}}{dt}=\frac{d\vec{p}}{dt}$$ Looking at the last expression (definition in ...
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1answer
17 views

A central force which enables a torque on a sphere - is it still conservative?

Consider the following example: Two spheres (one big, other small) standing vertically on ground. At first, the small sphere is on top of the big sphere. Then, it starts to roll w/o slipping to ...
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1answer
21 views

Velocities of points along an inextensible string

It is a well known constraint that velocities of points along an inextensible taut string or rod is constant. This is, for instance of use in the following problem: If a rod slides along the wall ...
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2answers
37 views

How does the earth do a negative work on a static body? [on hold]

If a body is in rest and the earth acts with a force on it 10 N Is there a negative work done by the earth though the body doesn't move? how? does it have a common thing with potential energy?
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60 views

Why is it easier to go uphill on a lower gear?

In cars as well as bicycles, when we are on a lower gear, the driving wheel (the one on the wheels) has a bigger radius compared to when on a higher gear. So on a lower gear the bike/car would move ...
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2answers
24 views

Understanding incompressibility (of rubber or viscoelastic material)

Literature gives a lot of explanation why rubber is incompressible. However, I still need some thinking to understand physical behavior of rubber or any such material. Often, incompressibility is ...
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1answer
73 views

How to formulate variational principles (Lagrangian/Hamiltonian) for nonlinear, dissipative or initial value problems?

Although this questions is very much math related, I posted it in Physics since it is related to variational (Lagrangian/Hamiltonian) principles for dynamical systems. If I should migrate this ...
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1answer
40 views

Computing the gravitational force on a planet in a particular system [on hold]

I have a system of four planets moving in a 2D plane. I'm trying to write some code (C++) to find the positions of these planets at time t=3. I'm probably going to attempt this via a leapfrog ...
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1answer
47 views

Given potentials, how does one find conserved quantities using Noether's theorem?

I've been asked to find the conserved quantities of the following 3D potentials: $U(\vec{r}) = U(x^2)$, $U(\vec{r}) = U(x^2 + y^2)$ and $U(\vec{r}) = U(x^2 + y^2 + z^2)$. For the first one, ...
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2answers
50 views

How to analyse this mass-spring system

I'm trying to analyze this mass-spring system -- i.e. write down the differential equation governing it. As you can see, there is a block of mass $m_1$ attached to a wall by an ideal spring of ...
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1answer
35 views

Potential Energy of Interaction Between a Sphere and a Particle Formula Derivation [closed]

A sphere of radius R has density described by ρ=ρ(r). Derive equation for pontetial energy of interaction between the sphere and some point particle of mass m which is at distance r from the center of ...
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1answer
99 views

Can a thrown egg chip (or break) a car windshield?

Is it possible to throw an egg with such speed that a car windshield will chip (just like with stone chips?) I have searched around for existing research in the area and have found that the impact ...
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1answer
30 views

What will happen to the center of mass of the human body when a person carries a weight with one hand?

What will happen to the center of mass of the human body when a person carries a weight with one hand a briefcase for example. Wouldn't the center of mass move horizontally towards the side carrying ...
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0answers
42 views

Proof that a traceless strain tensor is pure shear deformation

How can i proove that the traceless part of linear strain tensor $e$ in the Euler description: $$e_{i,j}={ 1 \over 2 } \left({ \partial u_i \over \partial x_j}+{ \partial u_j \over \partial x_i} ...
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2answers
62 views

Angular momentum consevation law [closed]

Consider two equal masses connected with a massless rod. This system is rotating around an axis, passing through the centre of mass of the system. This axis is not perpendicular to the rod. We know ...
2
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0answers
20 views

Would the torque required by a motor differ depending on where it connects to a frame?

Given a motor attached to a flat surface, aligned to the axis of a laptop screen and connected to the screen via an L shaped arm which is also connected to the motor shaft Would the torque required ...
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0answers
46 views

Stability of Mathieu's equation and parameteric resonance

I am given the following equation (Mathieu's equation) in my subject of Numerical Analysis : $$ \frac{d^2 x}{dt^2}=-\omega^2(1+\epsilon\cos(t))x $$ I am supposed to find those frequencies $\omega$ ...
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1answer
23 views

Elementary proof of the minimum number or parameters needed to uniquely identify a force-torque (aka wrench) in 2D vs. 3D

Since the term force-torque (aka wrench vector) is probably more common in Robotics than in Physics, let's try to start with a definition of what is sought: a force-torque is a parsimonious set (well, ...
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0answers
23 views

What is the direction of the force at the top of a cantilever structure? [closed]

What is the direction of the force from C on the big element ? (The force from B on the big element is oriented according (AB) because it is a cylinder and the weight is vertical at G)
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0answers
29 views

Motion Integrals of a Particle in a Force Field

I am trying to wrap my head around the following problem: A point particle is moving in a field, where its potential energy is U=-α/r. Find first motion integrals. In our university we have no ...
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0answers
24 views

Simple explanation of first and second class constraints with an example

Can someone give a simple physical example of first class and second class constraints? I mean, if you were giving a classical mechanics lecture for undergraduates, how would you explain this concept ...
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2answers
57 views

Symplectic structure and isomorphisms

In his book Mathematical Methods of Classical Mechanics, V.I. Arnold writes To each vector $\xi$, tangent to a symplectic manifold $(M^{2n},\omega^2)$ at the point $\mathbf{x}$, we associate a ...
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0answers
16 views

Trajectory of a boat given by $$r=\frac{d sec(\alpha)}{(sec\alpha + tan\alpha)^{V/V_{R}}}$$ [closed]

I need some help with this problem, I've tried using polar and cartesian coordinates but I dont know how to get the trajectory (I've already obtained the position, velocity and acceleration vectors as ...
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0answers
10 views

Non-dimensionalizing the “bead on a rotating hoop, with viscous damping” problem

This is not a homework question. Rather, this is an exercise I have taken up on myself. In particular, I am trying to find an algorithmic way to non-dimensionalize known equations, using the ...
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1answer
23 views

Does this massless spring affect the system?

I have to write out the differential equation modelling this system: There's a mass connected to a wall with a spring of spring constant $k_1$, sitting on a frictionless surface, with another spring ...
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0answers
22 views

Rotation of Thin street sign

I am attempting to complete a home question in which a shop sign in the shape of a thin rectangle of size p x q (with q being the longer side), and mass m, that rotates about an axis that passes ...
2
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0answers
19 views

Limits for the linear wave equation

In acoustics and continuum mechanics the following wave equation (for Speed of Sound $c$) for the pressure field $p$ is well-known: $\partial_t \partial_t p = c^2 \Delta p$. This wave equation can be ...
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5answers
2k views

How could a cord withstand a force greater than its breaking strength?

How could a 100 N object be lowered from a roof using a cord with a breaking strength of 80 N without breaking the cord?? My attempt to answer this question is that we could use a counter weight. But ...
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2answers
45 views

Energy drain in damped oscillator

Suppose we have a mass on a spring with a damping term. The equation of motion is given by: $$m \ddot{x} = -kx - c\dot{x}$$ I believe solutions are damped oscillations of the form: $$x = x_0 ...
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1answer
51 views

Mathematical pendulum in accelerating frame of reference [closed]

An aquintance of mine, who is a first year physics student was given a simple task as a homework-like task, which is about determining the ratio of periods between two equal-parameter mathematical ...
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2answers
47 views

Taking moments about two different points in a system of forces

If you have a system of forces and you take moments about two different points will the moment be the same?
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26 views

A ladder and a cube [duplicate]

I don't really understand how to start part two. Could some give me a hint? And no, this is not a duplicate of A twist on the leaning ladder problem. That question is regarding the first part, this ...
1
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1answer
19 views

Is the force of a lifting arm due to a piston an internal force?

When I was analyzing an excavator, I was wondering if the force that the piston exerts on the lifting arm is an internal or external force. I am a bit confused because the geometry of the system ...
-1
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1answer
140 views

How the center of gravity works in the picture? [duplicate]

How the center of gravity works in the picture? How the other parts of the body able to hold the bal;ance of the center of the gravity of the man?
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37 views

Derivable Concepts in Mechanics and Electromagnetism

In Classical Mechanics, one of the possible foundations is based on three concepts aka mass(equivalent to energy), length and time. This is a foundation because we can model everything ( pressure, ...
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0answers
36 views

Prove a transformation is a variational symmetry?

My question: How to prove the family of transformations of the $(t,q)$ space, given by $(t,q) \to (t,U(\epsilon)q)$, where $U(\epsilon) \in SO(3)$, is a variational symmetry? So it depends on $L$ by ...
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0answers
56 views

Deriving Snell's law via Lagrangian mechanics

A particle moves with kinetic energy $K_1$ in a region where its potential energy has a constant value $U_1$. After crossing a certain plane, its potential energy changes discontinuously to a new ...
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3answers
56 views

Can vertical SHM occur in a system of a mass between 2 springs between 2 vertical pillars? [closed]

The problem is detailed above. I have worked through problems involving SHM in the horizontal plane, but unsure how to go about it vertically. I know the weight component would need to be ...
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1answer
26 views

Why ingoing and outgoing impact parameters equal in elastic scattering?

Take the Rutherford scattering, as for example in this picture: What is the easiest way to show that the impact parameter "b" (see picture) is the same for the ingoing and outgoing trajectories? ...
3
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0answers
86 views

Chocolate dynamics

Now I have found a possible model on how to describe chocolate when it is chewed. It has to do with geometrical transformations when a curve $\gamma$ intersects a manifold $M$. The chocolate is ...
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0answers
20 views

Will the center of mass of the whole system change when object swims on curved surface?

In the example given here, the object can move on the frictionless surface of the sphere by changing its shape periodically. So will the center of mass of the whole system change after the object ...
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0answers
26 views

Force in colliding snooker balls

If a snooker ball is traveling at 2m/s and hits another ball, the first ball will stop dead and the second will accelerate instantaneously to 2m/s. F=ma, so this would seem to imply an infinite force. ...
1
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2answers
63 views

How to calculate the classical on-shell action for a harmonic oscillator? [closed]

So, short and sweet, I've been reading the path integrals book by Feynman and Hibbs, and one of the elementary problems they ask is to calculate the classical on-shell$^1$ action of a harmonic ...
2
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0answers
40 views

Rheological behavior of chocolate

If someone eats chocolate, the chocolate goes through the following configurations: $\chi_0:$ chocolate is solid and has a smooth Surface everywhere; the Riemann Tensor vanishes on every Point of the ...
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1answer
33 views

How to calculate the deceleration of two trains moving with the same velocity? [closed]

Two trains travelling on the same track are approaching each other with equal speeds of 40m/s. The drivers of the train begin to decelerate simultaneously when they are just 2km apart. If the ...
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2answers
80 views

How was time defined before we knew the speed of light was constant or in classical physics? [closed]

Nowadays, we now about $c$ the universal speed of light. This lets us define the notion of distance in terms of time (despite the fact that it works the opposite way for our common units.) Before ...
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1answer
69 views

Why Galilean spacetime is not $\mathbb{E}^4$?

In Newtonian mechanics the physical spacetime is a Galilean spacetime with an affine surjection $\pi : \mathbb{A}^4\to \mathbb{E}^1$ from affine space $\mathbb{A}^4$ to Euclidean space $\mathbb{E}^1$. ...
1
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1answer
66 views

How is this a gauge choice mathematically?

I've been reading an article about the "square cat", which is described as the system bellow Such system is a deformable body that can change $a$ and $\theta$ but has $b$ fixed. The article uses ...
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1answer
61 views

Instant centre of rotation for two connected gears

The two gears are have the angular velocities $\omega_1$ and $\omega_2$ respectively with respect to $Oxyz$. The task is to determine the angular velocity $\boldsymbol{\omega}$ of the arm ...