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Euler to quaternions transformation

Introduction:

Embarking on a celestial journey involves more than just a vessel and fuel; it requires a deep understanding of the fundamental equations that govern the dynamics of rocketry. Among these equations, the Tsiolkovsky Rocket Equation stands as a cornerstone, encapsulating the intricate relationship between mass, velocity, and the pursuit of the heavens. In this exploration, we dive into the mathematical depths, deriving and unraveling the Tsiolkovsky Rocket Equation.

The Tsiolkovs