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In this paper, we focus on a specific problem related to the calculus of variations, which deals with finding the Lagrangian function that, when used in the Euler-Lagrange equation, produces a given differential equation

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calculus-of-variations einstein hamiltonian jacobi jlm lagrangian friedmann

jacobi-and-lagrangian-formulation-of-the-classical-cosmological-equations's Introduction

๐Ÿ’ซIntroduction

a091f947-6547-4f37-922f-2243123c7cf0
  • ๐Ÿ‘‹ Hi, Iโ€™m Riddhiman Bhattacharya FRSA*

  • ๐Ÿ‘€ Iโ€™m interested in Physics and Mathematics

  • โšก Under Physics I'm interested in Cosmology, Quantum Mechanics and String Theory.

  • ๐ŸŒฑ Iโ€™m currently learning Python ๐Ÿ, Fortran and Matlab.

    *FRSA: Fellow of Royal Society of Arts, London, UK

๐Ÿ’ซ About Me

WhatsApp Image 2023-07-17 at 00 04 17

As I delve into the depths of my being, it may seem peculiar to describe myself using Physics concepts, but I delight in intertwining the realms of Physics and Mathematics into every aspect of my life.

As I imagine myself as a quantum particle, I find myself in a state of superposition, akin to Schrรถdinger's Cat. It's intriguing to think that until someone enters my room and observes me, my true state remains uncertain, existing as a combination of possibilities.

In this quantum analogy, the probability of finding me engrossed in reading a Physics paper in my room is high, just as it is for me doing Physics stuffs or engaging in coding/graphing.

Mathematically, I can be described by a wave function

lagrida_latex_editor (3)

where the square of its absolute value determines the likelihood of finding me in a particular state.

As I reflect on this quantum perspective, I recognize that my level of enthusiasm is intimately tied to my inherent creativity and thinking. It's these qualities, represented by matrix A, that contribute to shaping my state of mind.

lagrida_latex_editor (1)

In this formula, $C$ represents the inherent creativity, and $C_1, C_2, ..., C_n$ denote various aspects or facets of creativity that contribute to shaping your state of mind. Similarly, T represents thinking, and $T_1, T_2, ..., T_n$ represent different dimensions of thinking.

Moreover, there lies a mysterious challenge before me

lagrida_latex_editor (4)

waiting to be unraveled. I believe that cracking this enigma requires the profound tools of Mathematics (M) and Physics (P). By harnessing the power of these disciplines, I can navigate the unknown and bring clarity to the hidden truths.

HOBBIES

GRAPHING AND CODING

๐Ÿ“ˆ & ๐Ÿ‘จโ€๐Ÿ’ป I thoroughly enjoy coding and graphing as they allow me to unleash my creativity and create fascinating plots and artwork. Using languages like Python and graphing tools like Desmos, I can bring my ideas to life by combining mathematical equations with visual representation. It's an exhilariting experience that merges the logic world of coding and mathematics with the artistic flair, resulting in captivating and visually pleasing creations. With each line of code and graph, I dive deeper into a world where science and art beautifully intertwine, offering endless possibilities for exploration and expression.

image

There are lot more. Whenever I'm free I open Desmos Graphing and spend my time trying some form of creative things. I'll upload my works from time to time. Also I run a Youtube Channel where I upload the videos of the plots,and graphs. Make sure to visit it.

ASTROPHOTOGRAPHY

๐Ÿ”ญ Sky observation is a passion of mine. The beauty and mystery of the stars, planets, a
nd galaxies fascinate me. I love capturing these objects through my telescope and camera, and exploring the wonders of the universe. 
It's a intriguing experience that always leaves me in awe.
Close and Detailed Capture of the Moon
Close and Detailed Capture of the Moon
Jupiter
Capturing Jupiter- the Largest Planet in our Solar System
Moon-Venus Occulusion
Moon-Venus Occulusion on March 24th

DEBATE

๐ŸŽ™๏ธ๐Ÿ—ฃ๏ธ 

BLOGS AND ARTICLES

 ๐Ÿ“ I publish a basic and interesting physics [here](everlastingquestforphysics.wordpress.com) 
 aimed at engaging general students in science. My goal is to make 
 science more accessible and enjoyable for everyone, and I believe that by breaking down complex concepts and 
 making them easy to understand, I can help inspire a love of learning in my readers.

MUSIC: INSTRUMENTAL

  ๐ŸŽธ As a music enthusiast, I love diving into the world of instruments. 
  From the soothing melodies of Rabindrasangeet to exploring various genres, I enjoy experimenting on the guitar, synthesizer, tabla, and khol. Though my musical endeavors may not be regular, once I start with my Guitar, I get lost in a captivating journey of endless experimentation and musical exploration.

๐ŸŒ Social Media

I'm not very active in social media but here are my social media links

  1. Twitter
  2. YOUTUBE

GitHub Stats

riddhiman2005

ย riddhiman2005

riddhiman2005

GitHub Badge

Programming Languages

I'm learning a lot of things. Though I'm not expert in coding, I can do a little bit. Out of my own interest, I've learnt or to say am learning the enlisted languages

  1. JAVA
  2. Javascript
  3. C
  4. CSS
  5. C++
  6. Python
  7. Fortran
  8. Html
  9. Kotlin
  10. Rust

Everlasting Quest for Physics(EQP) is an initiative to provide a platform for HS students with like minded peers and teach, discuss courses which are not under normal school curriculum.

EQP-Logo
Everlasting Quest for Physics

The is the Website link where you'll find my blogs. They are mostly for general students sometimes made creative with added humor to invoke the interests for Physics and Maths among students.

Date of Foundation: 15th Feb,2022
Collaborators: Fun Learning Youth

  1. Instagram : Here, I regularly posts some Physics stuffs.

  2. Facebook

BOOKS

Everlasting Quest for Physics-I

This book, inspired by my friend Wrick Pal, is a culmination of my gratitude for his unwavering support and motivation.This book not only delves into my observational works in Physics but also explores topics beyond the school curriculum.

Physics is the philosophy to understand the functioning of the Universe at its most fundamental level using the tools of mathematics, everlasting curiosity and imagination.


The initial chapters of the book explore mathematical aspects, including Spherical Trigonometry. Moving forward, we discuss intriguing theorems such as Fourier's, Taylor's, and Euler's Theorems. Later, we delve into the fascinating realms of Relativity and Quantum Mechanics, specifically focusing on Schrรถdinger's Quantum World. The book concludes with a discussion on Cause-Effect Relationships, Cosmos under the Lenses of Thermodynamics, the darkness of night sky, the enigmatic nature of Time, and matter-antimatter's presence.

Throughout the text, I have strived to present explanations and insights, incorporating relevant examples, videos, and links to further explore these captivating subjects. From intriguing paradoxes to philosophical implications, this book seeks to illuminate the world of Physics, offering a unique perspective and emphasizing the interplay between mathematics and observation.

I've tried to engage readers in thought-provoking discussions on various paradoxes and their applications in quantum physics. The journey through these concepts may be challenging but ultimately rewarding, unveiling the intricate nature of the quantum world.

Geometric Kinematics in Lorentzian Geometry: Relativistic Motions and Their Characterizations

Screenshot (935)

In this work, I've focused on the study of three notable motions in General Relativity, Uniformly Accelerated Motion (UAM), Unchanged Direction Motion (UDM), and Uniform Circular Motion (UCM) which are well-established concepts in Classical Mechanics. UAM was explored in Lorentz-Minkowski spacetime L^4 and referred to as hyperbolic motion. However, I aim to extend the analysis of these motions to arbitrary spacetimes using modern Lorentzian Geometry techniques.

In Chapter 1, I have explained the essential tools of (differential) Lorentzian Geometry, including the notion of time orientation for a Lorentzian manifold, which is fundamental in defining spacetime. The main focus of Chapter 2 is to introduce the Fermi-Walker covariant derivative of an observer and the associated Fermi-Walker parallel transport. This enables the analysis of an observer that follows a UAM, where their 4-acceleration remains constant in a general spacetime. Such an observer can be geometrically characterized as a Lorentzian circle. I also explored how trajectories of uniformly accelerated observers can be represented as the projection of integral curves of a specific vector field defined on a particular fiber bundle over the spacetime. Moreover, I discussed assumptions that ensure the absence of singularities for inextensible UAM observers within a finite proper time. Chapter 2 also delved into the study of UDM and UCM in arbitrary spacetimes. I analyzed these three motions from the perspective of the corresponding ordinary differential equations that define each motion. Throughout the work, I emphasized the significance of accurate techniques from Lorentzian Geometry, particularly the Fermi-Walker connection, which provides each observer with a moving gyroscope in their relative space at each instant of their proper time. These advanced tools allowed me to gain a deeper understanding of the motions observed in General Relativity.

๐ŸŽจ ARTS

GRAPHING

1)
Graphing
Google

2)
Birthday Cake
Happy Birthday

3)
Flag Made through Equations and Graphs
Jai Hind
4)
Heart.-.Google.Chrome.2023-05-13.20-33-36.mp4

5)
YouTube
YouTube

6)
love
Heart

7)
Batman
Batman Equation

8)
Egg
Egg

9)
Bhai
Smile is the best medicine

10)
Ice Cream
Ice Cream

11)
Spider Web)
Spider Web
12)
Instagram
Instagram Logo
13)
Avengers
Instagram Logo

I'll update this section from time to time.

Coding

Check this repository of mine where I've all the Codes for these Pictures.

1) World Environment Day

image

This Diagram of the Tree is prepared by Python Coding. It's not perfect. Still, I thought to add it here.

2) Doraemon

Done using Python.

Doraemon
Hello Friends, my name is Doraemon

3) Rainbow

Done using Python

Rainbow
Rainbow

4) SIM of Revolution of Planets(using Html)- Very Basic*
Simulation.of.8.Planets.of.the.Solar.System.using.Html.mp4

YOUTUBE

I recently started uploading my Graphing works in Youtube Channel. I just do it for fun, and want to improve myself through suggestions of my viewers.

Here is the Link of the channel. YOUTUBE. I mostly upload my graphing and coding projects.

Contact

I can be contacted by my two mails given below

  1. [email protected]
  2. [email protected]

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