Dec 2021 to July 2022

Indian Institute of Technology, Bombay
Research Intern  

Successfully completed a Research Project at IIT Bombay’s NCAIR (National Centre for Aerospace Innovation & Research) under the mentorship and guidance of Professor Asim Tewari who is the HEAD of NCAIR.

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​During my research at IIT Bombay I realized there are various software packages that are built to aid physics learning and teaching and they have specific modules and solve several problems.

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​There are specialized physics packages which consists of a training simulation software and instructional materials that help students understand and explore the fundamental laws of physics and mathematical methods of investigation of the movement of celestial bodies. In contrast, the mathematical modelling software allow users to build mathematical models of physical problems and obtain corresponding solutions.

​I initially tried modelling of planetary motion using Maple Software.

However, I later learnt the Python Computing Language from scratch and decided to model the various motions on Python itself.

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My GitHub Account: https://github.com/aashnijoshi

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​​RESEARCHED AND USED PYTHON AS FOLLOWS :

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• Constructed a function that determines the next prime number after a number ’n’ wherein the value of n is inputted by the user.

• Calculated the root of a function using bisection method.

• Researched and understood the working behind Newton Raphson Method of calculating the roots and also implemented that in a python program.

• Researched about the time module in python and imported it for various programs to calculate the time of execution of the programs.

• Created a virtual Rock Papers and Scissors Game by importing the random function from the math module.

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​RESEARCHED ON LINUX & SHELL SCRIPTING TO UNDERSTAND:

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• The syntax of Linux and can now implement functions like pwd, cd, ls, cp, rm, echo, cat and the vi editor

• The basics of shell scripting and how it works.

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​​RESEARCH, ANALYSIS AND MODELLING FOR THE SOLAR & LUNAR ECLIPSES:

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• Analysed and understood the motion of the moon around the earth and the conditions necessary for solar and lunar eclipses to occur and thereby coded two programs that generate the date, time and place of all solar and lunar eclipses from 2001 to 2100 by importing python modules connected to astronomy.

• Created a program that will generate the length of the shadow of any object given the date, time, city and length of the object. The program generates the latitude and longitude simply by inputting the city from the user.

• Moreover, in addition to the length of the shadow, the program also calculates and prints the angle the shadow makes with the geographic north i.e. the direction of the shadow.
   

SUNDIAL CONSTRUCTION

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• Understood the working of the different types of sundials and manually constructed a sundial for Mumbai in accordance with its latitude. Manually constructed the dial as well as the pointer.

• Calculated and implemented the difference, in degrees, between every hour line and thereby designed the dial.

• Manually constructed the dial as well as the pointer. This Sun dial is now put up at the terrace of the NCAIR office for viewers to observe.

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MODELLING & ANIMATION OF THE SOLAR SYSTEM

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• Using the Pygame Module, created an animated program that depicts the motion of the first four planets around the sun.

• Not only was the mass of the sun considered in modelling the orbit, but also the mass of other planets was factored in as an average.

• Moreover, the orbits were modelled as elliptical and not simply circular. Distances of the planets from the sun was exactly to scale in the program.

• Successfully created a 3D model on Python of the Solar System with all the Planets around the Sun using Matplotlib. The size of the planets relative to each other was to scale with the exception of the sun.

• Distances of the planets from the sun was exactly to scale in the program.

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RESEARCH & ANALYSIS OF PLANETS — REVOLUTION & ROTATION:

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• Described why the plane of revolution of all planets as well as the direction of revolution is the same.

• Explained and Analysed three theories for the unusual rotation direction of Venus.

• Identified the angle between earth’s magnetic pole and spinning pole, between earth’s rotation axis to revolution plane and between plane of revolution of earth and plane of revolution of moon.

• Interpreted and explained the motion of moon around the earth regarding time of revolution as well as time of rotation and through a simulation, illustrated why we always face the same side of the moon.

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RESEARCH & ANALYSIS OF RECURSION:

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Understood the process of recursion and constructed several programs to develop a greater understanding of it:

• Checking if a number is prime or not.

• The power function — returns a^b for given values of a and b.

• Generating the Fibonacci Series.

• Calculating factorial of any number.

• Calculating the sum of all odd and even digits between two numbers.

• Generating prime triplets.

• Solving the Tower of Hanoi problem.

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RESEARCH & ANALYSIS OF PROJECTILE MOTION:

​Derived equations relating to projectile motion on basis of its initial velocity, angle, time period, maximum height, and angle of projectile:

• Designed a program that plots the path of a projectile given its initial velocity and angle with the horizontal using matplotlib.

• In addition, constructed two 3D plots of time vs velocity vs angle and range vs velocity vs theta for a given projectile.

• Also included an option for the user to select any planet in the solar system and thereby get the 3D plot for the projectile on that planet.

• Also structured a program such that upon entering a Range, this program generates 3 different combinations of initial velocity and angle with the horizontal that give the same range.

• However, we think of it as a cannonball shooting shots. A total of 3 shots are fired and the time interval between these shots is inputted from the user. The time period for the first cannonball is also inputted from the user. Not only does this program accurately calculate values that deliver the same range, but it is also error corrected.

• If the time interval between two cannonballs is more than the time period of the first, the program will generate an error message and call the input function again.

• As a continuation of the program above, using the Pygame Module, also created a program that traces the path of these three projectiles in an animated fashion with the particular time intervals factored in.

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​Thus, with the help of the above-mentioned computing languages, tools, software and research, I was able to easily, quickly and with sufficient accuracy, model and animate the various cases of motion of material points and bodies.