Here is a daily log for Jakob Grzesik from 2017.6.5 to 2017.8.5 in Saito Lab in Tohoku Univ.

## Daily schedule (tentative)†

• 09:00-09:30 Begin climbing to campus
• 09:30-09:35 Succumb to burning feeling in calves and take a break
• 09:35-10:00 Resume climb to lab
• 10:00-11:00 Finishing/continuing any work from previous day
• 11:00-12:00 Discussion with Shoufie-san
• 12:00-13:00 Lunch
• 13:00-13:30 Prepare for daily report presentation
• 13:30-14:30 Meeting with Saito-sensei
• 14:30-18:30 Start working on work for tomorrow's presentation and updating Pukiwiki

## Goal of the project†

• Synchronization of particle motion

This section is for posting questions from Haihao-san and answers from other group members.

• Please list here with some simple reasons or details.
• For every problem, give a tag double asterisks (**) in the code so that it will appear in the table of contents.
• For the answer, give a tag triple asterisks (***) in the code below the problem in order to make a proper alignment.
• List from new to old.

## Report†

This part is basically written by Yakub-san. Any other people can add this. Here the information should be from new to old so that we do not need to scroll.

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### June 12†

• Finished writing a Python program to approximate and graph solutions for coupled linear differential equations using the Runge Kutta method.

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### June 9†

• Discussed with Shoufie how to extend the Runge-Kutta algorithm I made for a system of a single differential equation to a system of many coupled differential equations. Learning how to better implement matrices in python looks like it'll be helpful.
• Found out that my derivation for Euler-Lagrange equation involving non-conservative forces had a mistake that led to different results than expected. Will be looking over and correcting it this weekend.

To do:

• Enjoy the weekend and check out the Kizuna Matsuri, which will be in town.
• Fix derivation of Euler Lagrange equation and apply it a simple situation to verify it works, and then apply it to the more complicated example I discussed with Saito-sensei on Thursday.
• Find damping of a system as a function of frequency.

### June 8†

• Solved problem for HW and did some more exercises with Lagrangian mechanics and ODEs.
• Learned about an example of synchronization phenomenon with Saito-sensei. Involved first getting equations of motion using Lagrangian mechanics, then applying Linear Algebra and differential equations. Ended up with system that was not analytically solvable and needed to be numerically approximated.
• Worked on deriving Euler-Lagrange equation in systems with non-conservative forces.

To do:

• Begin learning how to plot equations effectively. JSXGraph looks very promising, but difficult to learn.
• Design programs to numerically solve differential equation systems. Start off with Euler's method, than build upon that to do the Runge Kutta method.
• Solidify understanding of EL in non-conservative situation to the extent that I can follow and present the derivation.

### June 7†

• Walked to campus, took the right path, so it only took about 25 mins to make it to the lab.
• Plotted results for last night's HW with varying parameters.
• Practiced getting equations of motion for more complicated systems using Lagrangian Mechanics.
• Considered systems with damping forces and modelled motion using differential equations.

To do:

• Apply linear algebra and ODEs to solve a general second order differential equations problem.
• Learn how to solve ODEs and linear algebra questions using python(Start with Euler's approximation method).

### June 6†

• Walked to campus, got lost at campus. Took about 45 mins.
• Finished working on HW about action and the Euler Lagrange equation
• Worked on learning about differential equations.
• Worked on applying Lagrangian mechanics to double pendulum.
• Had lunch with Nulli-san at Espace Ouvert
• First "experiment": synchronization of vegetable can movement within a box due to forces exerted while carrying it and walking at a certain pace.

To do:

• Solve equations of motion for a box on a spring with some initial external force over a fixed period of time, both before and after external force is removed.
• Numerically solve ODEs in Python(perhaps using numpy and scipy packages).

### June 5†

• Shoufie-san picked me up from Urban Castle Kawauchi, took me to campus by subway (International Center -> Aobayama, 250 yen ~20 mins total)
• Nugraha-sensei helped me set up lab server access, mail client, etc.
• Got a quick bento lunch on campus and ate with Saito-sensei who played his ukulele
• Learned about Lagrangian mechanics, specifically in the context of a simple pendulum.
• Learned a bit about the general solutions to second-order differential equations.

To do:

• Learn what "action" in physics is
• Derive the Euler-Lagrange Equation