This article discusses the the selection and justification of the reference system and of the generalized coordinates for the kinematic scheme developed by of the manipulator taking into account these factors. The absolute (inertial) coordinate system associated with the center of the support member (eg turntable), joins the arm to the base machine and the subsequent coordinate system formed in accordance with the rules. On the whole, to describe the position of the investigated little detail of the manipulator in the space of generalized coordinates must be four and five right-hand orthogonal coordinate systems.
The aerodynamic experimental set TRMS (Twin Rotor MIMO System) is a strong nonlinear system, which has been taken by many scientists as an object to test modern control algorithms. The paper built a complete and explicit dynamic model for the TRMS based on dissociating TRMS into 3 subsystems, using homogeneous transformations in orthogonal coordinate systems to calculate the mass point’s position and velocity in component sub-systems; Euler - Lagrange equation was applied to model the dynamics for the object. Keywords— TRMS, dynamics, homogeneous transformation, mechanical system dissociation, Euler - Lagrange.
Algorithms for scaling and visualization of nucleotide sequences developed in this study allow identifying relationships between the biochemical parameters of DNA and RNA molecules with scale invariance, fractal clusters, nonlinear ordering and symmetry and noise immunity of visual representations in orthogonal coordinate systems. The algorithms are capable of displaying structures of the nucleotide sequences of living organisms by visualizing them in spaces of various dimensions and scales. Approximately one hundred genes (protozoa, plants, fungi, animals, viruses) were analysed and examples of visualization of the nucleotide composition of genomes of various species have been presented. The developed method contributes to an in-depth understanding of the principles of genetic coding and simplifying the perception of genetic information due to the algorithmic interpretation of the basic properties of polynucleotide fragments with visualization of the final geometric structure of the genetic code.
Dynamic Model of TRMS Based on Homogeneous Transformation and Euler-Lagrange Equation
