TITLE:
Qualitative Analysis of Solutions of a Nonlinear Biomechanical Model
AUTHORS:
Ifeoma D. Omoko, Ayinla A. Abdurasid, Jamiu R. Akewushola, Ola A. Salami
KEYWORDS:
Nonlinear Differential Equations, Biomechanics, Stability, Boundedness, Lyapunov Methods, Knee Joint
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.11,
November
29,
2024
ABSTRACT: The behavior of objects in motion is described by the equations of motion, which are basic concepts in mathematical physics. These equations are useful in explaining how forces and torques cause body components to move around a joint when applied to joint movement, especially in biomechanics. In the orthopedic industries, biomechanics is widely used to develop orthopaedic implants for a range of body joints, dental parts, external fixations, exoskeletons, and other medical uses. In this case, the motion of a phenomenon is described using a nonlinear differential model. One of the most effective approaches for describing the qualitative behavior of a dynamical system is the introduction of Lyapunov methods. Stability analysis and boundedness of solutions of a nonlinear differential equation model, particularly in the context of knee joint movement, entails analyzing how minor perturbations (like changes in force, position, or velocity) influence the behavior of the joint and remain within a finite range over time, respectively. The goal is to determine whether the system returns to a steady state (stable) or becomes unstable when subjected to these small changes. The effect of viscous damping, external input, and angular motions at different times in seconds are all controlled to govern the shank knee movement surrounding the knee joint. Numerical simulations with Matlab and Mathematica are drawn to demonstrate the effectiveness of the shank knee motion around the knee joint.