# Rotational dynamics of a free triatomic molecule

Rotational dynamics of a free triatomic molecule

This notebook explores the rotational dynamics of a triatomic molecule by numerically solving Euler’s equations for the free rotor to obtain the angular velocity in the body fixed frame,ω(t). Euler matrices R(Θ) are employed to express ω(t) in terms of the Euler angles and its time derivatives, Θ and . The solution of the first order differential equation =(ω(t),Θ) gives the Euler angles as functions of time Θ(t). Finally, the rotation of the molecule and its fixed coordinate frame, with respect to the space fixed frame, is obtained by applying the time dependent Euler rotation R(Θ(t)) to the position vector of the atoms of the molecule.

Θ

Θ

Θ

## Importing the data Wolfram Language online repositories

Importing the data Wolfram Language online repositories

## Space fixed coordinate frame

Space fixed coordinate frame

## Body Fixed Coordinate Frame

Body Fixed Coordinate Frame

## Differential equations for the rigid molecule

Differential equations for the rigid molecule

## Solving Euler Equations for random initial angular velocities

Solving Euler Equations for random initial angular velocities

## Euler angles and the rotation matrix

Euler angles and the rotation matrix

## Differential equation for the Euler angles

Differential equation for the Euler angles

## Define the rotating molecule and frame

Define the rotating molecule and frame

## The graphical representation of the rotational dynamics

The graphical representation of the rotational dynamics

Further Explorations

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