Three vs ER3D Euler Rotations in 3D

1. For a batter observation, all volumes are enlarged by many times (the range of gravity in the real universe is much larger, and the planet is much smaller, so don’t worry about breaking the Roche limit) 2. Users can add up to 7 Sun, and randomly distribute them to nearby spaces. 3. Users can add an asteroid matrix. Asteroids have no gravity (negligibly small in the reality) and are only affected by Suns. (Well, in fact, it is afraid that the cpu is limited, and it is impossible to calculate the mutual gravitational force of too many stars.) 4. The three-body system is very unstable, and it is prone to gravitational slingshot effect. If a star is too far away from other stars, it may never come back. 5. However, users can also turn on an additional r/10 parameter to increase the gravitational force of stars at a long distance and make it return to the system (after turning on the parameter, it can only be used for demonstration, and the data has no reference value).

Three-dimensional (3D) rotational kinematics are one of the most important, and yet also one of the most easily misunderstood topics of advanced mechanical engineering dynamics and trajectory simulation modeling. The ER3D mobile app aims to be a teaching aid for students and interested learners who want to understand these fundamental kinematics in an interactive and visually appealing setting, including in Augmented Reality (AR). Features of the app include: - Space Shuttle model for teaching a 3-2-1 rotation sequencee - Gyroscope model for teaching a 3-1-3 rotation sequence - Sliders to update 3-2-1 (yaw, pitch, and roll) or 3-1-3 (procession, nutation, and spin) angles - Globe Earth that may be rotated to visualize locations at different latitudes and longitudes - Context menus with text descriptions of the kinematic properties ER3D is free and open source, developed for iPhone, iPad, macOS, and VisionOS using SwiftUI and RealityKit.