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lagrangian
September 6, 2023
by rsroybaruah ADV-MATHEMATICS

Lagrangian and Lagrange’s Equation from Hamilton’s Principle in Classical Mechanics

Introduction to Classical Mechanics Classical mechanics is a cornerstone of physics, describing how objects move and interact with forces. It encompasses various formulations, each providing unique insights and tools for solving mechanical problems. O ...

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geodesics
September 3, 2023
by rsroybaruah ADV-MATHEMATICS

Geodesics: Shortest Path Between Two Points in a Curved Space

When we think about the shortest path between two points, we often envision a straight line on a flat surface. However, in the realm of curved spaces, the concept of the shortest path takes on a new form known as a "geodesic." Understanding geodesics is ...

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2
special cases
September 3, 2023
by rsroybaruah ADV-MATHEMATICS

Special Cases of Euler’s Equation: Calculus of Variation

Welcome, fellow math enthusiasts, to an intriguing journey through the world of the calculus of variations! Today, we will explore the special cases of Euler's Equation, a cornerstone in this field. Whether you are a seasoned mathematician or a curious l ...

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euler-lagrange equation
September 2, 2023
by rsroybaruah ADV-MATHEMATICS

Euler-Lagrange Equation in Calculus of Variations

Euler's equation, also known as the Euler-Lagrange equation, is a fundamental concept in the calculus of variations, a branch of mathematics that deals with finding the extremum (minimum or maximum) of a functional. In this context, a functional is a fun ...

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addition law of velocities
September 1, 2023
by rsroybaruah ADV-MATHEMATICS

The Relativistic Addition Law of Velocities or Velocity Addition Theorem

Introduction to the Addition Law of Velocities In our everyday experiences, velocities simply add up. If you're walking at 5 km/h on a train moving at 60 km/h, your speed relative to the ground is just 65 km/h. This intuitive rule, however, breaks dow ...

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2
length contraction
September 1, 2023
by rsroybaruah ADV-MATHEMATICS

Consequences of Lorentz Transformation – Length Contraction, Time Dilation and Simultaneity of Two Events

Introduction to Lorentz Transformation Welcome, fellow enthusiasts of the cosmos, to an exciting exploration of the consequences of the Lorentz Transformation. In the world of physics, few concepts are as mind-bending and transformative as those propo ...

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4
lorentz transformation
September 1, 2023
by rsroybaruah ADV-MATHEMATICS

Lorentz Transformation – Special Theory of Relativity

Welcome, curious minds, to an exhilarating journey through one of the most fascinating concepts in modern physics—the Lorentz Transformation within the realm of the Special Theory of Relativity. Whether you're a seasoned physicist or just someone with a ...

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1
variation
August 30, 2023
by rsroybaruah ADV-MATHEMATICS

Variation of a Function in Classical Mechanics

Calculus of variations, a branch of mathematics concerned with the problem of finding a function for which the value of a certain integral is either the largest or the smallest possible. The problem of Calculus of variations was first solved by Jacob ...

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2
maxwell's
August 27, 2023
by rsroybaruah ADV-MATHEMATICS

Maxwell’s Laws of Electromagnetism are Not Invariant Under the Galilean Transformation

Introduction: The Clash of Two Theories In the world of physics, different theories often intersect and sometimes clash, leading to new insights and advancements. One such clash occurs between the laws of electromagnetism, as formulated by James Clerk ...

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2
electromagnetism
August 25, 2023
by rsroybaruah ADV-MATHEMATICS

Electromagnetism, Laws of Electromagnetism, Maxwell’s Equations in Empty Space

Electromagnetism is a fundamental branch of physics that deals with the study of electric and magnetic fields and their interactions. It is a unifying theory that explains both electric and magnetic phenomena as manifestations of a single electromagnetic ...

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