[tag:classical-mechanics] entails the study of the trajectory of bodies under the influence of forces. More specific subtopics are: [tag:newtonian-mechanics], [tag:lagrangian-mechanics], [tag:hamiltonian-mechanics] for point particles and [tag:fluid-dynamics], [tag:statistical-mechanics] and ...
3
votes
3answers
189 views
Are quantum mechanics and determinism actually irreconcilable? [closed]
As a preface, I am not a physicist. I'm simply interested in abstract physics and fundamental principles of the universe and such. As such, if you can provide an answer for the layman (as ...
-1
votes
1answer
43 views
Leaning sticks on a horizontal surface [closed]
A body is composed of two straight pins that are joined at a right angle. They have lengths α and β and the mass per unit length is ρ. When the body is balanced on a flat surface, as shown, how large ...
4
votes
1answer
190 views
Constants of motion vs. integrals of motion
Since the equation of mechanics are of second order in time, we know that for $N$ degrees of freedom we have to specify $2N$ initial conditions. One of them is the initial time $t_0$ and the rest of ...
4
votes
4answers
140 views
Wheel locks and spinout
Imagine driving in a straight line on a ice lake, when you hit the brakes, if your goal is to stay in straight path with no spinout, which wheels would you choose to have locked: front or rear? ...
-2
votes
1answer
159 views
Work done to tighten a screw [closed]
We use a wrench to turn nuts on bolts because they require less force. Consider a hexagonal nut 1 cm in diameter. We can tighten this nut with one of two wrenches, wrench A with lever arm 10 cm and ...
0
votes
1answer
123 views
Why does weak equivalence principle say gravity is equivalent to acceleration?
I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
4
votes
2answers
108 views
Are Poisson brackets of second-class constraints independent of the canonical coordinates?
Say we have a constraint system with second-class constraints $\chi_N(q,p)=0$. To define Dirac brackets we need the Poisson brackets of these constraints: $C_{NM}=\{\chi_N(q,p),\chi_M(q,p)\}_P$ . Is ...
1
vote
3answers
87 views
Condition for closed orbit [closed]
I'd like to know when an orbit is closed. I know that, to have a closed orbit, there is a ratio that must be a rational number, but I don't know other things..
0
votes
0answers
93 views
Small oscillations: diagonal matrix [closed]
I'm solving an exercise about small oscillations.
I name $T$ the kinetic matrix and $H$ the hessian matrix of potential.
The matrix $\omega^2 T- H$ is diagonal and so find the auto-frequencies is ...
1
vote
2answers
148 views
Can a student with a heavy math background start learning physics with Goldstein's “Classical Mechanics”? [duplicate]
Can a student with a heavy math background start learning physics with Goldstein's "Classical Mechanics"?
Or is the book too obtuse with basic physics that I need to start elsewhere?
3
votes
3answers
123 views
Virtual differentials approach to Euler-Lagrange equation - necessary?
I'm currently teaching myself intermediate mechanics & am really struggling with the d'Alembert-based virtual differentials derivation for the Euler-Lagrange equation. The whole notion of, and ...
2
votes
2answers
251 views
Meaning of subscript in $V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$
This is probably a simple question, but what does the subscript $0$ mean in the following expression?
$$V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$$
1
vote
0answers
59 views
Limitations on the choice of axis of rotation regarding rolling wheels
Consider a situation where a wheel is rolling without friction on a level surface. Call the center of the wheel $C$, the point where the wheel contacts the ground $G$, and some arbitrary other point ...
0
votes
0answers
245 views
Problems and solutions to mechanics questions [closed]
I am taking a course called "analytical mechanics,” and I see similar courses listed as "theoretical mechanics.”
I was wondering if anyone would point me to Internet sources of solved example ...
1
vote
1answer
41 views
Please provide the simplest example you can think of, of generators of time evolution and generalized coordinates
I was reading the Wikipedia article about Noether's theorem and this thing popped out:
Then the resultant perturbation can be written as a linear sum of the
individual types of perturbations
...
2
votes
1answer
107 views
Sideways motion between a vertical launch from a planet and landing [duplicate]
I saw a video some days ago (Hello Kitty in Space) of a schoolgirl successfully launching a balloon into space which later popped and landed ~47 km from launch site.
If I vertically launch an object ...
1
vote
0answers
32 views
A question related to tractrix
I'm a novice to physics, so maybe it's rather stupid.
According to wiki, the tractrix could be considered a trajectory:
Suppose $AB$ is a stick on a smooth plane $\pi$, and the initial position of ...
5
votes
3answers
609 views
Why is tunneling not a classical idea?
There is no tunneling in the case of infinite potential barrier, but there is when we have a finite well. In the classical analog, in the first case we have a particle bouncing between to infinitely ...
-1
votes
1answer
79 views
Question about de Broglie Waves?
Is photon interaction , electrostatic interaction outside the nucleus and gravitational interaction is all due to electromagnetic waves ? and CAN be identified as with the de Broglie waves ?
I ...
6
votes
2answers
214 views
What are the reasons for leaving the dissipative energy term out of the Hamiltonian when writing the Lyapunov function?
I have a problem with one of my study questions for an oral exam:
The Hamiltonian of a nonlinear mechanical system, i.e. the sum of the kinetic and potential energies, is often used as a Lyapunov ...
6
votes
1answer
224 views
Three Pendulum Rotary Harmonograph
I'm trying to create a simulation of a three pendulum rotary harmonograph, the one you can see in action in this video or in these instructions.
As you can see in the video, there are 2 pendulum with ...
3
votes
2answers
218 views
The Double Integrator: Matching velocity and position as quickly as possible with only a limited amount of force available
If a body with mass $m$ begins at position $x_0$ with velocity $v_0$ and experiences a force that varies as a function of time $f(t)$ (and we ignore gravity, friction, and everything else that might ...
15
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11answers
974 views
Why quantum mechanics?
Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
2
votes
1answer
158 views
Find the Hamiltonian given $\dot p$ and $\dot q$
I have these equations:
$$\dot p=ap+bq,$$
$$\dot q=cp+dq,$$
and I have to find the conditions such as the equations are canonical. Then, I have to find the Hamiltonian $H$.
To answer to the first ...
-1
votes
1answer
78 views
Find generating function $F_1$ for canonical trasformation
I'd like to know the steps to follow to find the generating function $F_1(q,Q)$ given a canonical transformation.
For example, considering the transformation
$$q=Q^{1/2}e^{-P}$$
$$p=Q^{1/2}e^P$$
...
1
vote
2answers
73 views
How can I understand work conceptually?
I'm in a mechanical physics class, and I'm having a hard time understanding what the quantity of work represents. How can I understand it conceptually?
2
votes
1answer
55 views
Solution of motion in hamiltonian formalism
I have these canonical equations:
$$\dot p = - \alpha pq$$
$$ \dot q =\frac{1}{2} \alpha q^2$$
I have to find $q(t)$ and p$(t)$, considering initial conditions $p_0$ and $q_0$.
I thought to simply ...
4
votes
0answers
45 views
Animating the Bosonic String
I am interested in studying the classical solutions to the Bosonic string in flat 3+1 dim. spacetime by having them rendered a moving picture on a computer. This is partly for fun, and partly to ...
1
vote
2answers
179 views
Numerical torque calculation
Suppose I can compute interaction energy of two rigid bodies as a function of their coordinates of centers of masses and Euler rotation angles (total 6 + 6 degrees of freedom). Now I can numerically ...
7
votes
9answers
852 views
How to explain independence of momentum and energy conservation in elementary terms?
I'm trying to explain to someone learning elementary physics (16 year old) that linear momentum and energy are conserved independently. I'm not a professional physicist and haven't tried to explain ...
1
vote
1answer
74 views
Electric Flux Contradiction
I am currently reading about electric flux; and from this passage I am reading, I am sensing a bit of a contradiction:
"If the E-field is not perpendicular to the surface area, then the flux will be ...
0
votes
1answer
5k views
Formula for a ball rolling down an Inclined Plane
Suppose we set up an experiment where we have an inclined ramp, and a spherical basketball. If we were to assume the ball to be perfectly round, and rolls down in a vertical manner and the situation ...
5
votes
1answer
112 views
Rolling a deformed ring
Consider a ring rolling without slipping along a horizontal surface. Regardless of the speed of the ring, it is continuously in contact with the surface.
Let's deform the ring slightly so that it ...
3
votes
3answers
1k views
What is the physical meaning of diffusion coefficient?
In Fick's first law, the diffusion coefficient is velocity, but I do not understand the two-dimensional concept of this velocity. Imagine that solutes are diffusing from one side of a tube to another ...
2
votes
1answer
178 views
What if $F\neq \frac{dp}{dt}$?
I was thinking of this idea that maybe there are esoteric cases where the force is not given in classical mechanics as $F=dp/dt$ but as some function of $F=F(p,q,\dot{p},\dot{q})$
E.g, something ...
3
votes
3answers
182 views
Is there a mathematical relationship here or am I looking for relations when there are none?
When I was taking classical mechanics, we dealt a lot with pendulums, and orbiting bodies problems. This lead me to think about the two situations depicted above. Left: Shows two balls of equal mass ...
0
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0answers
47 views
An ideal toilet roll on a flat surface [closed]
Suppose we have an ideal toilet roll on a flat surface with the outer end of the roll fixed to the surface. After we give the roll an initial velocity such that the roll unwinds, what happens to the ...
1
vote
1answer
82 views
What does net mechanical efficiency mean?
I often see the term "net mechanical efficiency" used in literature, but I am not quite sure what it means, and what the difference is between it and "normal" efficiency. Take this sentence for ...
1
vote
2answers
336 views
Problem of Landau, Lifshitz - Mechanics - Integration of the Equations of motion [closed]
I'm studying Landau, Lifshitz - Mechanics. Could someone help me with this problem ? =)
Problem 2 (Page 27 3rd Edition) Determine the period of oscillation, as a function of the energy, when a ...
3
votes
1answer
111 views
all the 1-dimensional problems in newtonian mechanics are solvable?
i mean given a system with a conserved Energy in one dimension
$$ E= \frac{p^{2}}{2m}+V(x) $$
then the 'solution' to this problem is implicitly given by
$$ t(x)= \frac{1}{2m} ...
3
votes
1answer
156 views
Is there any case in classical mechanics where Newton's (strong) third law doesn't hold?
Is there any case in classical (non relativistic) mechanics where the strong form of Newton's third law does not hold (that is, reaction forces are not collinear)? For example, if we consider a system ...
0
votes
0answers
82 views
Elastic strings [closed]
Two elastic strings, $A$ and $B$, stretch by $30 \text{mm}$ and $60 \text{mm}$ respectively when a weight of $4 \text{N}$ is attached to each in turn. the strings are hung vertically from the same ...
1
vote
0answers
259 views
Lagrangian of pendulum with pivot point rotating about a circle [closed]
I just would like to know If I am on the right track with this stuff. I have scanned the work I have done, sorry if it is a little messy. Disregard the top most $\ddot x$
A disk of radius ...
0
votes
1answer
112 views
Question about non-holonomic geometric constraints
Suppose a point particle is constrained to move on the curve $y=x^2$. This would then be a non-holonomic geometric constraint since the particle has one degree of freedom and requires two coordinates ...
6
votes
9answers
2k views
Book about classical mechanics
I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical ...
2
votes
1answer
237 views
Calculating projectile range from known maximum height and time traveled
I've been stuck on this problem for many hours and I think I'm onto the right solution but I'm uncertain about my math.
I've got a projectile that I know its maximum height and it's hang time and I ...
20
votes
8answers
2k views
Why doesn't the bike fall if going with a high speed?
Why does the bike fall when its speed is very low or close to zero and is balanced when going with a high speed?
0
votes
2answers
135 views
Hamiltonian and non conservative force
I have to find the Hamiltonian of a charged particle in a uniform magnetic field; the potential vector is $ \vec {A}= B/2 (-y, x, 0)$.
I know that $$H=\sum_i p_i \dot q_i -L$$ where $p_i$ is ...
5
votes
3answers
893 views
Equivalent spring-constant for infinite square grid of springs
Consider an infinite square grid, where each side of a square is a spring following Hooke's law, with spring constant $k$.
What is the relation between the force and displacement between two points? ...
4
votes
1answer
162 views
Clarifications about Poisson brackets and Levi-Civita symbol
I need some clarifications about Poisson brackets.
I know canonical brackets and the properties of Poisson Brackets and I also know something about Levi-Civita symbol (definition and basic ...
