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Introduction
In a previous Physics Forums article entitled “How to Master Projectile Motion Without Quadratics”, PF user @kuruman brought to our attention the vector equation ##\frac{|V_0 \times V_f|}{g} = R## and lamented the fact that:
“Equally unused, untaught and apparently not even assigned as a “show that” exercise is Equation (4) that identifies the range as the magnitude of the cross product of the initial and final velocity divided by g.”
In this article, we reproduce and make use of equations presented in a 60s vintage article from the American Journal of Physics entitled “Convenient Equations for Projectile Motion”. The article abstract indicates:
“Quaternion multiplication of the basic vector equations for uniformly...
Quaternions are a mathematical concept used to represent rotations in three-dimensional space. They are used in projectile motion to calculate the orientation of an object as it moves through space.
Unlike other methods such as Euler angles or rotation matrices, quaternions do not suffer from gimbal lock, which can cause errors in calculations. They also have a more intuitive geometric interpretation.
Yes, quaternions can be used to calculate the trajectory of a projectile. By combining the quaternion representation of the object's orientation with the equations of motion, the position and orientation of the object can be determined at any point in time.
No, quaternions are not necessary for accurate projectile motion simulations. Other methods such as Euler angles or rotation matrices can also be used. However, quaternions may offer advantages in terms of efficiency and accuracy in certain situations.
Converting between quaternions and other rotation representations can be done using mathematical formulas or conversion functions provided by software libraries. It is important to understand the differences between the representations and their limitations in order to make accurate conversions.