*Article* **Kinematics in the Information Age**

#### **Brendon Smeresky 1, Alexa Rizzo 1 and Timothy Sands 2,\***


Received: 27 June 2018; Accepted: 21 August 2018; Published: 27 August 2018

**Abstract:** Modern kinematics derives directly from developments in the 1700s, and in their current instantiation, have been adopted as standard realizations ... or templates that seem unquestionable. For example, so-called *aerospace sequences* of rotations are ubiquitously accepted as the norm for aerospace applications, owing from a recent heritage in the space age of the late twentieth century. With the waning of the space-age as a driver for technology development, the information age has risen with the advent of digital computers, and this begs for re-evaluation of assumptions made in the former era. The new context of the digital computer defines the use of the term "information age" in the manuscript title and further highlights the novelty and originality of the research. The effects of selecting different Direction Cosine Matrices (DCM)-to-Euler Angle rotations on accuracy, step size, and computational time in modern digital computers will be simulated and analyzed. The experimental setup will include all twelve DCM rotations and also includes critical analysis of necessary computational step size. The results show that the rotations are classified into symmetric and non-symmetric rotations and that no one DCM rotation outperforms the others in all metrics used, yielding the potential for trade space analysis to select the best DCM for a specific instance. Novel illustrations include the fact that one of the ubiquitous sequences (the "313 sequence") has degraded relative accuracy measured by mean and standard deviations of errors, but may be calculated faster than the other ubiquitous sequence (the "321 sequence"), while a lesser known "231 sequence" has comparable accuracy and calculation-time. Evaluation of the 231 sequence also illustrates the originality of the research. These novelties are applied to spacecraft attitude control in this manuscript, but equally apply to robotics, aircraft, and surface and subsurface vehicles.

**Keywords:** Phoronomics; mechanics; kinetics; kinematics; direction cosines; Euler angles; space dynamics; digital computation; control systems; control engineering
