Strange solar systems #4:

Three suns dance in the sky above,
as they have since long ago
Tracing out a figure-eight,
they warm us down below.

It's said our planet's lucky,
That it wandered through the void
What life there was was trapped within
by encroaching bitter cold.

Alone and frozen till by chance
It came upon these stars
And with the heat of three small suns
The world we know evolved.

#worldbuilding #poetry #solarsystem #strangesolarsystems #3bodyproblem #classicalmechanics

Inspired by Christopher Moore's solution to the 3 body problem with equal masses. https://web.archive.org/web/20181008213647/http://tuvalu.santafe.edu/~moore/braids-prl.pdf

#PhysicsFactlet
The dynamics of a rigid sphere can be surprisingly complicated. In fact, beside rotating around an axis, the sphere can also precess (i.e. the axis of rotation is itself rotating) and nutate (i.e. the axis of rotation oscillates back and forth).

Euler's angles are particularly useful to describe such motion, as:
* Rotation is a change in the third Euler angle.
* Precession is a change in the first Euler angle.
* Nutation is a change in the second Euler angle.

#Physics #ClassicalMechanics #EulerAngles #Visualization

In #classicalMechanics, we are in the non-inertial reference frames part. That means I get to build a #python model of Earth's tides.

https://rjallain.medium.com/visualizing-tidal-forces-with-python-2b28cdce3413

Giuseppe Luigi Lagrangia was born in 🇮🇹 Turin (the Kingdom of Sardinia) on this day in 1736 (237 years ago). He later moved to 🇫🇷 France, naturalized French and adapted his name to Joseph-Louis Lagrange. He made significant contributions to the fields of analysis, number theory, and classical and celestial mechanics. Lagrange was one of the creators of the calculus of variations, deriving the Euler–Lagrange equations for the #extrema of functionals.
#ClassicalMechanics #Lagrange #NumberTheory

Hamiltonian field equations:
\[\boxed{\boxed{\dot\phi_i=+\dfrac{\delta\mathcal{H}}{\delta\pi_i},\ \dot\pi_i=-\dfrac{\delta\mathcal{H}}{\delta\phi_i}}}\]
The field analogue of the Hamiltonian formulation of classical mechanics!
#Hamiltonian #classicalmechanics #field #quantumfield #fieldequations #functional #theoreticalphysics #differentialequations

Hamiltonian field equations:
\[\dot\phi_i=+\dfrac{\delta\mathcal{H}}{\delta\pi_i},\ \dot\pi_i=-\dfrac{\delta\mathcal{H}}{\delta\phi_i}\]
The field analogue of the Hamiltonian formulation of classical mechanics!
#Hamiltonian #classicalmechanics #field #quantumfield #fieldequations #functional #theoreticalphysics #differentialequations

The (Newtonian) #Physics or #ClassicalMechanics of #ChangeManagement according to the #kihbernetic worldview:

The #Force required to put the change in motion is proportional to its #Mass or how large the change is; because the bigger the change the more #Friction it creates. The #Gravity, or how immediate the necessity to change is, will also increase the friction of the #ResistanceToChange.

However, once the change is put in motion, the #Acceleration produced by the mass’s #Inertia will start “pulling” the change by itself and only minimal force will need to be applied to #Control that the change is moving in the right direction and/or with the right speed of change.

#PhysicsFactlet
A large number of double pendula starting with very similar initial conditions and four 2D projections of their (4-dimensional) phase space.
#Visualization #Physics #PhaseSpace #ClassicalMechanics

#catflap #isaacnewton #mechanics #classicalmechanics #cats

#PhysicsFactlet
If you drive a (damped) harmonic oscillator at low frequency, the oscillations will follow the forcing. If the frequency increases the oscillations will start lagging behind, and (if you drive it with a frequency higher than the resonant frequency of the oscillator) they will be exactly out of phase with the forcing.
#Physics #ClassicalMechanics #HarmonicOscillator #Resonance

New #physics #classicalmechanics #lagrangian video
https://youtu.be/EyjZZ3cnkuI

I am transferring parts of my previous hand-written notes into a markdown notetaking app as backups and will casually share these notes on mastodon.

And again, I'm quite a newbie in physics, and my posts are very trivial. My mastodon posts will serve as some memory refresh tool for myself, and may not be very informative to others. But of course, I welcome any related discussion and corrections.

Anyway, below is my note on Central Force Problem.
#classicalmechanics
#physics
#notes

New #physics video from my #classicalMechanics series on #Lagrangian - a half swinging atwood machine

https://youtu.be/2rfKrTwhrGk