Kinematic Approach as an Alternative Way to study the Properties of Curves
Kinematic Approach as an Alternative Way
to study the Properties of Curves
Manukyan Vardan
Nikoghosyan Gagik
Key words: problem, physical, analysis, polygon, curve, equation, trajectory, length
The trajectories of various points in simple mechanical systems with kinematic constraints often represent well-known curves studied in mathematics courses. However, this fact is only noted at the stage of curve representation. Once the mathematical equation of the curve is obtained, the motion that generated it is generally no longer taken into account. All questions concerning the curve are then addressed using this equation along with the necessary mathematical knowledge and tools. On the other hand, in certain kinematics problems in school and university physics courses, we sometimes encounter requirements that seemingly go beyond the scope of physics and are purely mathematical in nature. For example, we may need to determine the radius of curvature of the trajectory of a body thrown at an angle at certain points. In such cases, of course, although determining the desired quantity is primarily of mathematical interest, it can also be obtained using purely kinematic methods. Thus, kinematics apparently contributes to the understanding of mathematical realities.
The following article demonstrates the feasibility of determining certain mathematical characteristics of curves through kinematic analysis of the movements that form them. This constitutes the scientific and methodological novelty of the work. The examples discussed highlight the interdisciplinary connections that play a significant role in the learning process.
DOI: https://doi.org/10.58726/27382923-2025.2-137