This book presents, in a uniform way, several problems in applied mechanics, which are analysed using the matrix theory and the properties of eigenvalues and eigenvectors. It reveals that various problems and studies in mechanical engineering produce certain patterns that can be treated in a similar way. Accordingly, the same mathematical apparatus allows us to study not only mathematical structures such as quadratic forms, but also mechanics problems such as multibody rigid mechanics, continuum mechanics, vibrations, elastic and dynamic stability, and dynamic systems. In addition, the book explores a wealth of engineering applications.

Quadratic Forms.- Rigid Body Dynamics.- Continuum Mechanics. Strain and Stress Tensor.- Modal Analysis.- Stability (Elastic and Dynamic).- Dynamical Systems.

Sorin Vlase is a Full Professor of Mechanics (1996) at Transylvania University of Bräov, Romania. He obtained his Dipl.-Ing degree in Automotive Engineering at the Transylvania University of Bräov(1976) and a licence in Mathematics at the University of Bucharest (1982). He was researcher at the Truck Factory ROMAN SA (1976-1978) and  at the Research Center in Automotive Engineering INAR SA (1978-1980).  He become Doctor in Engineering Sciences (Mechanics) in 1989 and obtain his habilitation in Automotive Engineering at the University of Pitesti (Dr.-hab.) in 2014. From 2012 become member of the Romanian Academy of Technical Science. In 2004 he become the Head of the Department of Mechanical Egineering at the Faculty of Mechanical Engineering in the Transylvania University where he still work. 

Marin Marin is a Full Professor of Mathematics at Department of Mathematics and Computer Science, Transilvania University of Brasov, Romania.

Andreas Öchsner is a Full Professor of Lightweight Design and Structural Simulation at Esslingen University of Applied Sciences, Germany. Having obtained his Dipl.-Ing. degree in Aeronautical Engineering at the University of Stuttgart (1997), Germany, he subsequently served as a research and teaching assistant at the University of Erlangen-Nuremberg from 1997 to 2003 while working to complete his Doctor of Engineering Sciences (Dr-Ing.) degree. From 2003 to 2006, he was an Assistant Professor at the Department of Mechanical Engineering and Head of the Cellular Metals Group affiliated with the University of Aveiro, Portugal. He spent seven years (2007-2013) as a Full Professor at the Department of Applied Mechanics, Technical University of Malaysia, where he was also Head of the Advanced Materials and Structure Lab. From 2014 to 2017 he was a Full Professor at the School of Engineering, Griffith University, Australia and Leader of the Mechanical Engineering Program (Head of Discipline and Program Director).