Activities in Analytical Mechanics

This is a loose collection of independent activities in classical mechanics, special relativity, as well as Lagrangian and Hamiltonian mechanics. Each activity is provided with solutions, further comments and fitting literature.

The activities were create as part of my exercise class for the lecture Allgemeine Mechanik held by Prof. Dr. Renato Renner (institute of Theoretical Physics, ETH Zurich, Switzerland) in the fall semester of 2021.

For more infos, see here (german page).


In my spare time I take images of the moon, stars, galaxies and other night sky objects with my Celestron telescope and either a Nikon DSLR camera or a ZWO ASI astro camera. You can find more details and all my images here. Below is an overview of my best images as well as my latest image.

Some of my best images so far: globular cluster m92, the moon, the Orion nebula (left to right)

M51 - Whirlpool Galaxy

M51 is a spiral galaxy in the constellation Canes Venatici. It is accompanied by a smaller, irregular galaxy which we can see on the left on one of the spiral arms.

M51 - Whirlpool Galaxy
M51 - Whirlpool Galaxy, taken on 2021-06-14. Celestron CGX EdgeHD 925, ZWO ASI 294 MC pro cooled astro camera, ZWO ASI 120MM guide camera, Celestron guide scope. 25x5min ~ 2h 5min, Gain 200, -10°C

NGC3628 - Hamburger Galaxy

NGC3628 is one of the three galaxies in the Leo triplet. It is a spiral galaxy we see edge-on.

NGC3628 - Hamburger Galaxy
NGC3628 - Hamburger Galaxy, taken on 2021-04-04. . 25x5min ~ 2h 5min, Gain 300, -10°C

ETH Semester Project on the Shadow
of a Rotating Black Hole

In the last semester (spring 2021) of my BSc physics at ETH Zürich, I wrote a semester project in theoretical physics on the shadow of rotating black holes. The shadow of a black hole is the completely black area in the sky an observer sees when looking at an unobstructed black hole; the shape and size depends on the properties of the black hole and can even be used to infer some of these properties. The project is a literature review of fundamental as well as recent research in the field. As such, it can serve as a structured introduction to the field of black hole shadows.

Learn more here.

Kerr shadows
The shadow edge of various rotating black holes (colours distinguish spin parameters, green is zero, red is maximal), seen from various inclination angles θO. This is fig. 3 of the semester project.

Random Mandelbrot Image of the Day

Each day, a little program I made renders a randomly chosen part of the mandelbrot fractal and uploads the image here. See here for past images and more information.

mandelbrot image
center: 0.244066 + -0.571305i, width: 0.0003

About me

Sébastien C. Garmier, 1999

Master student of physics at ETH Zurich (since 2021)

teaching assistant in quantum mechanics II at ETH

hobby astrophotographer

Bachelor of Science ETH in Physics (2021)

Matura diploma Kantonsschule Wohlen AG, Switzerland (2017)

Sébastien Garmier

photo: Janosch Abel


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