The objective of this book is an attempt at presenting and solving the known from the classical mechanics two and three dimensional single mass mechanical and mathematical vibration models in a higher order dimensional space. The common algorithm derived here for motion transformation is a geometrical transformation by means of projection of the vectors in the higher order dimensional space. The study can be applied successfully in many engineering fields and in physics and in astronomy, where the motion of the celestial bodies can be described by using the common algorithm. It is known in celestial mechanics that the bodies move usually in a curved surface or in a curved space. That is why the common algorithm can be applied successfully in the description of motion in the curved space and easily transformed into 3D or 4D space for a suitable analysis. These problems can have a philosophical aspect as well in cases when the space is considered as a curved one like around the black holes and the dwarfs in cosmos. Any kind of a trajectory of motion can be transformed successfully in a higher order dimensional space and vice verse by means of applying of the common algorithm.