[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 ...
4
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2answers
797 views
Rigid body dynamics joints
I can't seem to find any info on connected rigid bodies by a joint. Can someone explain the basics to me? I'm trying to do a little research to find out how feasible it would be to implement 3d ...
0
votes
2answers
108 views
Geometrical interpretation of complex eigenvectors in a system of differential equations
Let's consider a system of differential equations in the form
$$\dot{X} = M X$$
in two dimensions ($X = (x(t), y(t))$).
In the case that $M$ has real values, it is easy to give a geometric ...
4
votes
1answer
92 views
Liouville's theorem and gravitationally deflected lightpaths
It is customary in gravitational lensing problems, to project both the background source and the deflecting mass (e.g. a background quasar, and a foreground galaxy acting as a lens) in a plane.
Then, ...
4
votes
1answer
439 views
What are examples of classical physical systems having polynomial observables of degree greater than 2?
Specifically: What are empirically well-understood examples of (integrable) Hamiltonian systems whose Hamiltonians include polynomial expressions, in the canonical coordinates $\{q^i,p_i\mid ...
2
votes
1answer
74 views
What is the distance traveled
the red dots represent a side view of path traveled, F is downward force and the tool used here is a pen placing parallel to the coin
I have newly started to study mechanical physics. based on study, ...
2
votes
1answer
54 views
Pendulum Wave Period
Recently I've seen various videos showing the pendulum wave effect. All of the videos which I have found have a pattern which repeats every $60\mathrm{s}$.
I am trying to work out the relationship ...
2
votes
1answer
133 views
What is actually a resonating vibration and resonance?
What is actually a resonating vibration and resonance?
I have searched many books and made Google search too but couldn't understand it clearly.
2
votes
1answer
165 views
Additional accelerating force during take off of a rocket?
During the take off of a rocket, the exhaust produces some pressure below the rocket, which gives an additional force. How large is this force in comparison to the force produced directly by the ...
0
votes
1answer
25 views
Inclined plane question
An object, mass $m$ is placed on an incline, angle $\theta$. System is at equilibrium. coefficients of static and kinetic frictions are $\mu_s$ and $\mu_k$ respectively. Then:
1) What is the Total ...
0
votes
1answer
51 views
Stopping distance of two objects with equal Kinetic Energy
I'm working on a problem regarding two objects with the same kinetic energy.
Two objects with masses of $m_1$ and $m_2$ have the same kinetic energy are both moving to the right. The same constant ...
0
votes
1answer
75 views
Higher order covariant Lagrangian
I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at ...
0
votes
1answer
104 views
Do all black holes spin in the same direction?
My question is as stated above, do all black holes spin the same direction?
To my knowledge, the spin in the direction of the spin of the matter that created them. Another similar question was asked ...
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 ...
-1
votes
1answer
79 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
$$q=Q^{1/2}e^{-P}$$
$$p=Q^{1/2}e^P$$
...
6
votes
0answers
247 views
Classical mechanics: Generating function of lagrangian submanifold
I have a short question regarding the geometrical interpretation of the Hamilton-Jacobi-equation.
One has the geometric version of $H \circ dS = E$ as an lagrangian submanifold $L=im(dS)$, which is ...
4
votes
0answers
191 views
Extended Born relativity, Nambu 3-form and ternary (n-ary) symmetry
Background: Classical Mechanics is based on the Poincare-Cartan two-form
$$\omega_2=dx\wedge dp$$
where $p=\dot{x}$. Quantum mechanics is secretly a subtle modification of this. By the other hand, ...
4
votes
0answers
54 views
Scaling arguments for the Contact mechanics between two elastic spheres
I am studying a bit granular dynamics and I have seen that two spheres of radius $R$ in contact with a contact area of radius $a$ would need an applied force $F$ on this two spheres that is nonlinear ...
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 ...
2
votes
0answers
40 views
When can a center of mechanical momentum frame be found for an electromagnetic system?
In classical mechanics, a center of mechanical momentum frame can always be found for a system of particles interacting with one another locally. For an electromagnetic system where the charges ...
2
votes
0answers
32 views
When is classical mechanics valid for describing motion of atoms?
In Molecular Dynamics simulations, the Newton's equation of motion is used to calculate the time evolution of system. Once, I read in an introductory text that when the thermal de Broglie wavelength ...
2
votes
0answers
59 views
Approximations in simple pendulum
In the approximation $$-(g/ \ell) \sin \theta \approx -(g/ \ell) \theta $$ we make an error $R$ which is $O(\theta ^3)$. If i did well my calculations it is estimated by $$R\leq|(g / ...
2
votes
0answers
67 views
Classical scattering of two particles by a Yukawa potential
A point-like particle $A$, coming from minus spatial infinity, heads at another one, $B$, with an impact parameter of $b$.
Initial momenta are $p_A$ and $p_B=0$.
They repel each other via a Yukawa ...
2
votes
0answers
148 views
Normal modes of oscillation: how to find them
Are normal modes the eigenvectors of the matrix $(\omega ^2 T- V)$ where $T$ is the matrix of kinetic energy and $V$ is the matrix of potential energy?
Is it the only way to express them?
How can I ...
2
votes
0answers
109 views
Stiffness tensor
Let's have a stiffness tensor:
$$
a^{ijkl}: a^{ijkl} = a^{jikl} = a^{klij} = a^{ijlk}.
$$
It has a 21 independent components for an anisotropic body.
How does body symmetry (cubic, hexagonal ...
2
votes
0answers
93 views
Eternal clocks and 4D spacetime crystals
There was a recent article about the creation of 4D spacetime crystals based on recent theory proposed by Frank Wilczek. This theory is based on breaking time translational symmetry which basically ...
2
votes
0answers
160 views
include the stretch of the spring own weight in potential energy for spring pendulum?
we are given a problem with spring with its own mass $m$. I am confused how to set up the
PE term in the Lagrangian.
Assume the spring has length of $L_{0}$ when it is laying on a table
horizontally. ...
2
votes
0answers
542 views
Forces and torques about the CENTER OF MASS of a physical pendulum
I'm currently stumped by the following situation. Say we've got a rectangular physical pendulum (think ruler with a hole-punch at one end).
It's trivial to analyze the motion of the pendulum with the ...
2
votes
0answers
147 views
Why do control moment gyroscopes exhibit “torque amplification”?
There are a number of articles that describe the benefits of using control moment gyroscopes (CMGs) over reaction wheels in inertial navigation applications. One of the primary benefits of using a CMG ...
2
votes
0answers
374 views
Bungee jump physics
Question:
A bungee jumper jumps from a bridge. The length of the loose rope is 30 m. When the jumper reach the lowest point possible, the rope stretches 10 m. What is the final stretch of the rope, ...
1
vote
0answers
42 views
Why is the angle of impact complementary to the angle of launch in the simple equations for the range of a projectile?
I'm using the standard equation for the range of a projectile:
\begin{align}
d &= \frac{v\ \text{cos}\theta}{g} \left( v\ \text{sin}\theta + \sqrt{v^2\ \text{sin}^2\theta + 2gy_0}\right)
...
1
vote
0answers
16 views
Acceleration by spherical particles (micron-scale) by an external force
I am looking for an expression for the velocity of a micron sized (1 - 10 micron diameter) sized particles under accelerating forces.
I have aerosols in mind.
This is what I have in mind
The ...
1
vote
0answers
70 views
Torque, lever and mass
The Force used in a catapult is exerted near its axis.
If we double the length of the arm of the catapult, but still use the same Force at the same point as before near the same axis, does the ...
1
vote
0answers
44 views
Closed-form equation for orientation and angular velocity over time
If a rigid body, rotating freely in 3d, experiences no friction or other external forces and has an initially diagonal inertia matrix $\mathbf{I}_0$ (with $I_{11}>I_{22}>I_{33}>0$) and ...
1
vote
0answers
60 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 ...
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 ...
1
vote
0answers
20 views
On Bolte's semiclassical law
i have seen on internet the following, for $ E >> 1 $ the Eigenvalue Staircase can be approximated by $ N(E)= \frac{1}{\pi}argZ(1/2+i \sqrt E ) $
...
1
vote
0answers
71 views
How can I model a polyatomic molecule as a system of coupled oscillators?
(Classical Mechanics)
Let's say I have a polyatomic molecule, what is the best way for finding the equations of oscillations if they are bounded by a torsion spring?
0
votes
0answers
47 views
Getting started with Landau Physics course
I want to learn Physics in my own time. I am an electrical engineer, working in the same field and am tremendously interested in Physics. I have heard a lot about the 10 book series of Landau ...
0
votes
0answers
27 views
stable equilibrium in the system
I'm trying to understand the solution of the following problem.
A solid cube of uniform density and sides of b is in equilibrium on top of a cylinder of radius R. The planes of four sides of the ...
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votes
0answers
235 views
How to find angular velocity of a point inner a circumference
Let's consider a cicumference that have the center in the origin of axes and rotates around x-axes. Let's stick a bar in a point $A$ of this circumference and at the end of the bar let's stick a mass ...
0
votes
0answers
72 views
How does an oscillating particle in a non-inertial reference frame appear?
The general question is : given an oscillating particle in a non-inertial reference frame:
How would it appear from outside the non-inertial reference frame ?
How would an observer inside that ...
0
votes
0answers
47 views
Finding an efficient strategy for walking
Let's say you are already walking at a maximally efficient combination of pace and stride (or $\omega$ and $X_0$ I guess) but you need to reach your destination faster. Should you increase/decrease ...
0
votes
0answers
67 views
What are the details of this variational calculus solution?
This answer includes the problem:
Suppose you have a 2-d bullet going very fast through a 2-d gas. The gas molecules reflects specularly off the bullet, making glancing collisions. What shape of ...
0
votes
0answers
132 views
Sound waves. Relating the displacement to the pressure function
I am trying to understand some notes my professor has typed up. He writes that we can write a sound wave in terms of the variation of pressure in a medium over time using the function
$$ p(x, t) = P_0 ...
0
votes
0answers
99 views
Assume a spool rolls down a slope with its body (not its ends) in contact with the slope
I was doing a little mental exercise and imagined the above scenario. I can intuitively see that in the described case, the smaller the diameter of the spool body, the larger the proportion of the ...
0
votes
0answers
34 views
Does the direction of a rocket relative to an orbiting mass reduce the orbiting mass' orbital velocity?
Does a rocket taking off in the same direction of an orbiting mass (asteroid to planetary size) reduce the mass' orbital velocity versus the same rocket taking off in the opposite direction of the ...
0
votes
0answers
84 views
Aerodynamic drag on a cannonball?
I'm trying to build a ballistics simulation where I shoot a cannonball. I want to allow for drag and am trying to work out the math to do so.
I can work the drag out using $F = Cd\times S\times ...
0
votes
0answers
74 views
References for circular restricted 3 body problem?
Does anyone know of any good references for the CR3BP -- the circular restricted 3 body problem? Emphasizing on real-life applications, and interpretation of the numerical solutions? Thank you. There ...
