When moving an object in three-dimensional space, it is necessary to determine the direction the object will move. This is referred to as the direction of A⃗, or the axis of rotation.
When A⃗ is vertical, the object will not move in any other direction except down. When A⃗ is horizontal, the object will not move in any other direction except left or right.
Determining which way A⃗ is at any given time can be tricky. There are many ways to do this, and most are dependent on your programming language of choice and how you implement them.
This article discusses some ways to identify the axis of rotation in two dimensions. Some of these methods also apply to three dimensions, but some do not.
The direction of A⃗ is opposite the direction of B⃗
Imagine that the object is at position 1, and that A⃗ is the direction in which A⃗ is moving. If the object is at position 2, then A⃗ has to be moving in the opposite direction, or B⃗.
If you were to stand at position 1 and point in the direction of A⃗, then at position 2 you would have to point in the opposite direction, or B⃗.
This is because when you stand at position 2, you are looking down at position 1. When an object moves from position 1 to position 2, the only way to see this movement is if you point in the opposite direction of A⃗.
To make it even clearer, imagine that you are standing at position 1 and pointing in the direction of A⃗. Then, someone moves you to position 2 and points you in the opposite direction of B⃗.
The direction of A⃗ is closer to the direction of C⃗
Imagine A⃗ is at position 1 and C⃗ is at position 2. You are at position 3, looking in the direction of A⃗. Which direction best approximates the direction of A⃗ when the object is at position 1?
The answer is the direction of C⃗!
Imagine that you are standing at point A, facing point B. You turn to your right and face point C, then point A is to your left. Point B is in front of you, so you turn left to face it.
Now imagine that you are standing at point A, facing point B. You turn to your right and face point C, then point A is to your left. Point B is behind you, so you turn around to face it.
In both cases, you faced a different direction to face the same object but got a different answer due to your own personal orientation.
The directions are all different from each other
In physics, the term “direction” refers to a specific value of a coordinate. Coordinates are values that describe location, such as east–west (coordinate: latitude) and north–south (coordinate: longitude).
There are three coordinate axes in physics: east–west (longitude), north–south (latitude), and up–down (height). All of these axes have a direction, which can be described by a single number.
When an object is at position one, the A⃗ axis is defined as the axis that points toward the front of the object. The A⃗ axis is also called the longitudinal axis or fore-and-aft axis. In aerodynamics, this refers to the horizontal direction air travels as it passes over an aircraft.
The A⃗ is always perpendicular to the ground, regardless of where on earth you are. To determine which direction best approximates the direction of A⃗ when the object is at position one, we must first understand what this means.
The object has no clear directional pattern
In this case, the best approximation of the direction of A⃗ when the object is at position 1 is any direction. Because there are no clear directional patterns, any direction would be a good choice.
If there were a consistent pattern, like always turning right, then choosing any direction except right would be correct.
Because there is no clear pattern or rotation, this object is said to have no handedness. Handedness refers to which side of the object faces outwards or away from the innermost part. Objects that face a certain way are said to be oriented towards that way.
You may have heard people say that something is left-handed or right-handed, which refers to oriented objects. An object can be oriented in more than one way, like upside down and sideways at the same time.