This guide provides a foundational understanding of roll, pitch, and yaw, the three axes of flight. To delve deeper into this topic, here are some valuable resources:

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Roll pitch yawrotation matrix

The phase velocity $v$ of light changes transitioning from one medium to a different density medium according to its refraction index $n$ and the refraction angle to the incident is dictated by Snell's law:

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If the boundary entry and exit surfaces of the medium are not parallel to each other, like the prism case, you have to algebraically add their difference to the exit angle. Snell's law does not change.

An airplane doesn’t move in isolation – these rotations are often combined to achieve specific maneuvers. For instance, a coordinated turn involves a combination of roll and pitch. The pilot uses ailerons to bank the aircraft, then adjusts the elevators to maintain altitude throughout the turn. Similarly, yaw with coordinated aileron input helps fine-tune the direction during a turn, preventing skidding or slipping.

Yawing is similar to shaking your head side to side. It’s the rotation of the aircraft around the vertical axis, swinging the nose left or right. This movement is akin to steering a boat. The control surface responsible for yaw is the rudder, located on the vertical stabilizer (the fin). By deflecting the rudder left or right, the pilot disrupts the airflow over the vertical stabilizer, causing the aircraft to yaw in the opposite direction. While yawing doesn’t directly affect altitude, it plays a crucial role in coordinated turns. By using the rudder in conjunction with ailerons, the pilot ensures the airplane turns smoothly without sideslipping.

Roll pitch yawEuler angles

Imagine a seesaw tilted at one end. That’s essentially pitching! Pitching refers to the movement of the aircraft up or down along the lateral axis. The pilot controls pitch using the elevators, hinged flaps on the horizontal stabilizer (the tailplane). By raising or lowering the elevators, the pilot alters the angle of attack of the wings, which in turn, affects the amount of lift generated. Raising the elevators increases the angle of attack, generating more lift and causing the airplane to climb. Conversely, lowering the elevators decreases the angle of attack, reducing lift and initiating a descent.

For a beam of light, dispersion will cause different wavelengths of light to bend in different angles, but they will all bend in the same sense.

And the ray within the prism would bend away from the new normal at the new interface, corresponding to another clockwise rotation. ($\phi_2 < \theta_2$)

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The light then exiting the medium and returning to the initial medium regains whatever phase velocity $v$ it had in this medium and therefore also to its initial incident angle.

Understanding and coordinating roll, pitch, and yaw is the foundation of successful flight control. These axes are the building blocks that allow pilots to navigate the skies with precision and grace. Whether you’re a future aviator or an aviation enthusiast, grasping these concepts unlocks a deeper appreciation for the remarkable science and skill involved in flying.

Think of a majestic eagle performing a barrel roll. That’s roll in action! It’s the rotation of the aircraft along its longitudinal axis, tilting the wings from level flight to a banked position. This banking motion allows an aircraft to turn while maintaining lift. The control surfaces responsible for roll are the ailerons. These are hinged flaps located on the trailing edge of each wing. By moving the ailerons in opposite directions, one aileron lifts while the other lowers, creating an imbalance in lift between the wings. This differential lift causes the airplane to roll, initiating a turn.

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Whenever I see a 2D drawing of dispersion occurring when light travels through a solid prism, I see the rays get bent downwards on entry and downwards on exit again. For example here: https://www.wikiwand.com/en/Dispersion_(optics) To my understanding of optics when entering a medium with a higher optical density, the ray should get bent towards the normal of the surface, rotated CW and CCW when entering one with a lower IOR. However, the drawings suggest that it gets bent in the same direction upon entry and exit.

In reference to this figure, the incident ray should bend towards the normal, which would mean a clockwise rotation ($\phi_1 < \theta_1$)

Base image source: https://www.detailingwiki.org/detailing-miscellaneous/what-is-refractive-index/attachment/snellslaw1/

Ever wondered how airplanes defy gravity and perform graceful maneuvers? The secret lies in mastering roll, pitch, and yaw – the three fundamental axes of flight. Imagine your airplane as a three-dimensional object; these axes define its rotational movements around its center of gravity.