A particular challenge in the conceptual design of direct-from orbit delivery systems is the seemingly well-known kinematics retain fallacies whose efficacies are reduced over great distances. Rotation about the local wing of an aerospace vehicle is almost never the pitch angle, yet modern application of kinematics often assumes such (with accompanying angular error). The same assertion is usually true about the nature of roll and yaw angles. Expressing motion in coordinates of rotating reference frames necessitates transformation between reference frames, and one such transformation is embodied in the Direction Cosine Matrices (DCM) formed by a sequence of three successive frame rotations. One of two ubiquitous sequences of three rotations used to construct the DCM involves first a rotation around the inertial z-axis, then intermediate y-axis, then finally about the body’s x-axis; a sequence commonly called the “aerospace sequence” or the a “3-2-1 rotation sequence”. The second ubiquitous sequence is the so-called “orbital sequence” or “3-1-3 rotation sequence” with rotations about the inertial z axis first, then about the intermediate x-axis, then finally about the body z-axis. This manuscript evaluates which sequence is the most advantageous for an object starting in space and then travels through the atmosphere to a target on the Earth’s surface. Six degrees of freedom of vehicle motion were simulated starting in orbit with a given thrust and commanded maneuver. The simulation performs all twelve possible rotation sequences (transforming inertial coordinates to body coordinates) with comparison by computational burden and error representing rotations about body axes (roll, pitch, and yaw respectively). Simulation precision is validated using the quaternion normalization condition indicating near machine precision (0.9\times{10}^{-15}) and reveals the so-called 132 rotation is the most accurate with an average error of 0.14° and a computational time of 0.013 seconds: resulting in a 97.95% increase in accuracy over the so-called 321 rotation and a 99.84% increase over the so-called 313 rotation.

Understanding the mechanism, how entirely new (EntNew) gene/protein or the first ancestral gene/protein of a family was created, should be one of the most important issues in the biological sciences. However, the mechanism is totally unknown still now. On the other hand, it is well known that mature protein is generally rigid and one catalytic center exists on the protein. Creation of such a mature EntNew gene/protein should be, of course, carried out through random process, because it cannot be designed in advance. However, the EntNew gene/protein never be created by random polymerization of the respective monomeric units, because of the extraordinary large sequence diversities of ~10¹⁸⁰ and ~10¹³⁰, respectively. Protein 0^th-order structure or a specific amino acid composition, in which immature but water-soluble protein can be produced even through random process, holds the key for solving the difficult problem. As it was fragmentally described in the previous papers how and where EntNew gene/protein was created, I describe in detail in this review three processes generating EntNew gene/protein with some flexibility under three genetic codes, the universal genetic code, SNS primitive code and GNC primeval code, and discuss why the mature gene/protein could be created through the processes.