Aspects of Collinearity Property in Mechanics

Main Article Content

Răzvan-Bogdan Itu
Prof. Mihaela Toderaș

Abstract

Interdisciplinarity encourages students to make connections between different academic disciplines, fostering a deeper understanding of complex real-world problems. By integrating various subjects, students are able to develop critical thinking skills and apply their knowledge in practical ways. This approach not only enhances their learning experience but also prepares them for the challenges they may face in their future careers. In the paper, a strong connection between mathematics and mechanics has been demonstrated. It is important to note that the discussion of this topic is just scratching the surface of the many aspects that can be explored. This example highlights the principle of continuous learning and the endless possibilities for acquiring new knowledge in any field. The process of knowledge is infinite and always open to new contributions. By integrating knowledge from different disciplines, individuals can gain a holistic understanding of complex concepts and phenomena. This interdisciplinary approach fosters critical thinking skills and encourages creative problem-solving, enabling learners to tackle real-world challenges with a broader perspective. Additionally, the collaboration between disciplines promotes innovation and encourages the development of new ideas and solutions. This paper presents aspects regarding the application of the collinearity property in mechanics. The laws of motion of a rigid body, scalar functions of time are meant, which determine, in any moment of the motion, the position of the body in relation to a benchmark through the examples taken in the study were taken from point kinematics and rigid kinematics, also studying how the velocity and acceleration of the points of the solid body vary, in relation to the same reference system.

Downloads

Download data is not yet available.

Article Details

How to Cite
[1]
Răzvan-Bogdan Itu and Prof. Mihaela Toderaș , Trans., “Aspects of Collinearity Property in Mechanics”, IJEAT, vol. 13, no. 5, pp. 17–24, Jun. 2024, doi: 10.35940/ijeat.E4450.13050624.
Section
Articles

How to Cite

[1]
Răzvan-Bogdan Itu and Prof. Mihaela Toderaș , Trans., “Aspects of Collinearity Property in Mechanics”, IJEAT, vol. 13, no. 5, pp. 17–24, Jun. 2024, doi: 10.35940/ijeat.E4450.13050624.
Share |

References

P. Balbiani, L.F. del Cerro, “Affine geometry of collinearity and conditional term rewriting”. In: Comon, H., Jounnaud, JP. (eds) Term Rewriting. TCS School 1993. Lecture Notes in Computer Science, vol 909. Springer, Berlin, Heidelberg, 1995, https://doi.org/10.1007/3-540-59340-3_14.

P. Balbiani, V. Dugat, L. Fariñas del Cerro, A. Lopez, Eléments de géométrie mécanique. Hermès, Paris, France, 1994.

P. Bratu, Mecanică teoretică, IMPULS Publishing House, București, 2006.

Collinear Vectors: Definition, Condition, Formula with Proof. Available: https://testbook.com/maths/collinear-vectors.

H.S.M. Coxeter, S.L. Greitzer, Collinearity and Concurrence. Geometry Revisited. Washington, DC: Math. Assoc. Amer., 1967, pp. 51-79. ch. 3.

De Marco P Júnior, C.C. Nóbrega, Evaluating collinearity effects on species distribution models: An approach based on virtual species simulation. PLoS ONE 13(9): e0202403, 2018, https://doi.org/10.1371/journal.pone.0202403

G.A. Dirac, Collinearity Properties of sets of points, The Quarterly Journal of Mathematics, Volume 2, Issue 1, 1951, pp. 221–227, https://doi.org/10.1093/qmath/2.1.221

I.Love, The symmetry properties and collinearity of the magnetogyric, hyperfine splitting and magnetic susceptibility tensors, Molecular Physics, 30:4, 1975, 1217-1220, DOI: 10.1080/00268977500102761

G. Lemaître, “Regularization of the three-body problem”, Vistas in Astronomy, Volume 1, 1955, p. 207-215, https://doi.org/10.1016/0083-6656(55)90028-3.

C. H. Mason, W. D. Perreault, Collinearity, Power, and Interpretation of Multiple Regression Analysis. Journal of Marketing Research, 28(3), 1991, p. 268–280. https://doi.org/10.2307/3172863 .

R. Nisbet, G. Miner, K. Yale, “Numerical Prediction”, Editor(s): Robert Nisbet, Gary Miner, Ken Yale, Handbook of Statistical Analysis and Data Mining Applications, 2nd ed. Academic Press, 2018, p 187-213, ch.10. https://doi.org/10.1016/B978-0-12-416632-5.00010-4.

R. Sfichi, Caleidoscop de fizică, Albatros Publishing House, București, 1988.

V. Titov, Some properties of Lemaitre regularization. II isosceles trajectories and figure‐eight, Astronomische Nachrichten, 10.1002/asna.202114006, 343, 3, 2021.b.

V. Titov, Some properties of Lemaitre regularization: Collinear trajectories. Astronomische Nachrichten, 342, 3, 2021.a.

R. Voinea, D. Voiculescu, V. Ceaușu, Mecanică. 2nd ed. E.D.P., București, 1983.

E.W. Weisstein, Collinear. From MathWorld-A Wolfram Web Resource. Available: https://mathworld.wolfram.com/Collinear.html

C. Wenqi, G. Pillonetto, Dealing with Collinearity in Large-Scale Linear System Identification Using Gaussian Regression. arXiv:2302.10959 [stat.ML] Machine Learning (stat.ML). Cornell University. 2023. https://doi.org/10.48550/arXiv.2302.10959

R.R. Wilcox, Robust Regression, Editor(s): Rand R. Wilcox, Introduction to Robust Estimation and Hypothesis Testing (Fifth Edition), Academic Press, 2022, pp. 577-651, ch.10. https://doi.org/10.1016/B978-0-12-820098-8.00016-6 .

https://www.preferatele.com/docs/matematica/1/interpretarea-geomet16.php

https://www.scritub.com/stiinta/matematica/

https://smartician.ro/interdisciplinaritatea-sau-care-sunt-prietenii-matematicii/

Abdel-Wahab, A. M. (2020). Experimental Work for Evaluation the Time Saving Between Different GPS Techniques for Makkah- Jeddah Region. In International Journal of Innovative Technology and Exploring Engineering (Vol. 9, Issue 9, pp. 313–324). https://doi.org/10.35940/ijitee.i7206.079920

Aswal, P., Singh, R., kumar, R., Bhatt, A., & Raj, T. (2020). Resolving the four – Bar Link Mechanism by Kinamatics and Revolving Angle Solution. In International Journal of Recent Technology and Engineering (IJRTE) (Vol. 8, Issue 5, pp. 1003–1009). https://doi.org/10.35940/ijrte.e6069.018520

Rizvi, Dr. S. S. H. (2019). Isomorphism and Automorphism in Closed Kinematic Chains. In International Journal of Engineering and Advanced Technology (Vol. 8, Issue 6, pp. 2457–2460). https://doi.org/10.35940/ijeat.f8547.088619

Ganesh, Dr. E. N. (2022). Analysis of Velocity Measurement of Radar Signal in Space Vehicle Application using VLSI Chip. In Indian Journal of VLSI Design (Vol. 2, Issue 1, pp. 16–20). https://doi.org/10.54105/ijvlsid.c1207.031322

Mustofa, B., & Hidayah, R. (2020). The Effect of on-Street Parking on Vehicle Velocity and Level of Service at Cik Di Tiro Street Yogyakarta. In International Journal of Management and Humanities (Vol. 4, Issue 5, pp. 99–102). https://doi.org/10.35940/ijmh.e0534.014520

Most read articles by the same author(s)

<< < 1 2 3 4 5 6 7 8 > >>