This monograph examines Soviet operational centers of gravity during Operation Barbarossa, the German invasion of the Soviet Union in 1941. Specifically, the examination focuses in two areas: (1) German planning for Operation Barbarossa; (2) the operational objectives selected for the second phase of the campaign. The second phase was selected because it was during this phase that the focus of the German military effort became diverse. Two competing strategies within the German political and military command structure caused this. While political-ideological and economic factors influenced one, purely military concerns influenced the other. In the end, the Germans diluted combat power in phase two towards three operational objectives: Moscow, Leningrad, and the Ukraine. Thus, the research question for this monograph is: Which, if any, of the German operational objectives for the second phase of the campaign were also Soviet operational centers of gravity? The analysis of operational objectives uses Colonel William Mendel’s and Colonel Lamar Tooke’s analytical model called “Operational Logic: Selecting the Center of Gravity.” Potential centers of gravity are analyzed using a validity and a feasibility test. This monograph concludes that Moscow was the operational center of gravity for the campaign by virtue of its direct and intrinsic relationship to the strategic center of gravity—the Soviet Military.

Development of the Weight versus Moment C.G. Grid

Capitalises on the wealth of mathematical knowledge students already possess because of their familiarity with the scorekeeping and motion in sports. In this way, the book takes advanced concepts such as exponents, vector multiplication, and the unit circle to relate them to students everyday lives. While the book is meant to appeal to students who might not otherwise choose to study algebra, it employs highly challenging material, much of which is not taught until engineering school. Thus the book also provides a window to the professional world. Applications in accounting, aeronautical engineering, civil engineering and other fields are presented along with the sports examples.