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master's thesis
Dinamika ljudskog tijela
Zagreb: University of Zagreb, Faculty of Science, 2025. urn:nbn:hr:217:031620
Smoljan, Marin
University of Zagreb
Faculty of Science
Department of Mathematics

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Smoljan, M. (2025). Dinamika ljudskog tijela (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:031620

Smoljan, Marin. "Dinamika ljudskog tijela." Master's thesis, University of Zagreb, Faculty of Science, 2025. https://urn.nsk.hr/urn:nbn:hr:217:031620

Smoljan, Marin. "Dinamika ljudskog tijela." Master's thesis, University of Zagreb, Faculty of Science, 2025. https://urn.nsk.hr/urn:nbn:hr:217:031620

Smoljan, M. (2025). 'Dinamika ljudskog tijela', Master's thesis, University of Zagreb, Faculty of Science, accessed 22 March 2025, https://urn.nsk.hr/urn:nbn:hr:217:031620

Smoljan M. Dinamika ljudskog tijela [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2025 [cited 2025 March 22] Available at: https://urn.nsk.hr/urn:nbn:hr:217:031620

M. Smoljan, "Dinamika ljudskog tijela", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2025. Available at: https://urn.nsk.hr/urn:nbn:hr:217:031620

Metadata
TitleDinamika ljudskog tijela
AuthorMarin Smoljan
MentorMarko Vrdoljak (mentor)
Committee memberMarko Vrdoljak (predsjednik povjerenstva)
Committee memberPavle Goldstein (član povjerenstva)
Committee memberEduard Marušić-Paloka (član povjerenstva)
Committee memberHrvoje Šikić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2025-02-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu je demonstrirano kako možemo modelirati pokrete ljudskog tijela koristeći Lagrangeov pristup gibanju sustava krutih tijela, te način na koji možemo od skice pokreta doći do Euler-Lagrangeovih jednadžbi, u koje su dodane i generalizirane sile i momenti. Krenuli smo od definiranja krutih tijela s pripadnim relativnim koordinatnim sustavima i opisom njihovog međusobnog odnosa. Računanjem kinetičke i potencijalne energije svakog tijela smo odredili Lagrangeovu funkciju, odnosno... More Euler-Lagrangeove jednadžbe za dvije generalizirane koordinate. Time smo dobili model u kojem se dva međusobno spojena kruta tijela gibaju pod utjecajem sile teže, to jest dvostruko njihalo. Da bi u model dodali i sile mišića, definirali smo generalizirane sile Qi za svaku generaliziranu koordinatu i ubacili ih na desnu stranu Euler-Lagrangeovih jednadžbi. Sustav diferencijalnih jednadžbi drugog reda smo svođenjem na sustav diferencijalnih jednadžbi prvog reda numerički rješili u programu Octave, koristeći funkciju ode45. Program je napravio i animaciju pokreta, te ispisao graf s generaliziranim koordinatama i brzinama kroz vrijeme. Pokazali smo jedan zanimljiv način korištenja event funkcije za zaustavljanje programa, te na kraju iz već izračunatih sila, i numerički izračunate akceleracije dobili i reakcijske sile u šaci i laktu. Less
Abstract (english)
In this work, it was demonstrated how we can model the movements of the human body using Lagrange's approach to the motion of a system of rigid bodies, and the way we can get from the diagram of motion to the Euler-Lagrange equations, to which generalized forces and moments are added. We started by defining rigid bodies with the corresponding relative coordinate systems and a description of their mutual relationship. By calculating the kinetic and potential energy of each body we... More determined the Lagrange function, that is, the Euler-Lagrange equations for two generalized coordinates. This resulted in a model in which two connected rigid bodies move under the influence of gravity, that is, a double pendulum. To add the muscle forces to the model, we have defined the generalized forces Qi for each generalized coordinate and added them to the right side of the Euler-Lagrange equations. By reducing the system of second-order differential equations to a system of the first-order differential equations we have numerically solved it in the Octave program, using the function ode45. The program also created an animation of the movement, and printed a graph with generalized coordinates and speeds through time. We have shown an interesting way of using the event function for stopping the program, and finally, from the already known forces, and numerically calculated accelerations we have calculated reaction forces in the hand and elbow. Less
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:031620
Study programmeTitle: Financial and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2025-02-12 07:56:44
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