The aim of this course is to introduce students to the fundamental principles of kinematics and dynamics of a rigid body, kinematics and dynamics of complex particle motion, mass geometry, and the basic theorems and laws governing the dynamics of a material system.

Upon successful completion of this course, students should be able to: • Describe different types of body motion, including translational motion, rotation about a fixed axis, rectilinear motion, spherical motion, and general body motion. They should also determine kinematic characteristics such as angular velocity and angular acceleration, as well as the velocity and acceleration of individual points on a body. • Solve kinematic problems related to the complex motion of a point. • Determine the center of mass and moments of inertia for a material system and a rigid body. • Formulate expressions for momentum and angular momentum. • Determine the kinetic energy of a material system and a rigid body. • Apply theorems on changes in momentum, angular momentum, and kinetic energy for material systems and rigid bodies. • Analyze the dynamics of the relative motion of a particle. • Formulate differential equations and solve first- or second-order dynamic problems in translational motion, rotation around a fixed axis, and plane motion of a rigid body.

Kinematics of a rigid body: Translational motion, rotation around a fixed axis, rectilinear motion, spherical motion, and general motion. Kinematics of complex particle motion. Dynamics of complex particle motion. Mass geometry. General theorems and laws governing the dynamics of a material system and a rigid body. Differential equations of body motion: Translation, rotation about a fixed axis, and plane motion of a rigid body.

Kinematics of a rigid body: Translational motion, rotation around a fixed axis, rectilinear motion, spherical motion, and general motion. Kinematics of complex particle motion. Dynamics of complex particle motion. Mass geometry. General theorems and laws governing the dynamics of a material system and a rigid body. Differential equations of body motion: Translation, rotation about a fixed axis, and plane motion of a rigid body.

Defined by the study program curriculum

[1] Mladenović, N., 1996. Mechanics 2: Kinematics, Faculty of Mechanical Engineering, Belgrade. [2] Mladenović, N., Trišović, N., 2015. Dynamics, Faculty of Mechanical Engineering, Belgrade. [3] Simonović, M., Mitrović, Z., Golubović, Z., 2011. Mechanics – Kinematics, Faculty of Mechanical Engineering, Belgrade. [4] Mitrović, Z., Simonović, M., Golubović, M., 2011. Mechanics – Particle Dynamics, Faculty of Mechanical Engineering, Belgrade. [5] Pavišić, M., Golubović, Z., Mitrović, Z., 2011. Mechanics – System Dynamics, Faculty of Mechanical Engineering, Belgrade. [6] Mladenović, N., Mitrović, Z., Stokić, Z., 2007. Collection of Problems in Kinematics, Faculty of Mechanical Engineering, Belgrade. [7] Trišović, N., Lazarević, M., 1999. Handbook for the Exercises in Mechanics: Statics and Kinematics, Faculty of Mechanical Engineering, Belgrade. [8] Vuković, J., Simonović, M., Obradović, A., Marković, S., 2007. Collection of Problems in Dynamics, Faculty of Mechanical Engineering, Belgrade. [9] Pavišić, M., Stokić, Z., Trišović, N., 1998. Handbook for the Exercises in Mechanics: Particle Dynamics and System Dynamics, Faculty of Mechanical Engineering, Belgrade. [10] Written Lectures.

Total assigned hours: 70

New material: 30
Elaboration and examples (recapitulation): 0

Auditory exercises: 30
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 8
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 0
Test: 0
Final exam: 2

Activity during lectures: 0
Test/test: 60
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 40
Requirement for taking the exam (required number of points): 30

Mladenović, N. Mechanics 2, Kinematics, Faculty of Mechanical Engineering, Belgrade, 1996. ; Mladenović, N., Trišović, N. Dynamics, Faculty of Mechanical Engineering, Belgrade, 2015,; Vuković, J., Simonović, M., Obradović, A., Marković, S., A collection of tasks in dynamics,, MF Beograd, 2007.; Pavisic, M., Golubovic, Z., Mitrovic, Z. Mechanics - system dynamics, Faculty of Mechanical Engineering, Belgrade, 2011.; Mladenović, N., Mitrović, Z., Stokić, Z., A collection of tasks in kinematics, Mašinski fakultet, Beograd, 2007.