Transient Energy of an Individual Machine PART II: Potential Energy Surface

In this second paper, the individual-machine potential energy surface is established. The constant- $\theta _{i}$ angle surface of the machine is found in the angle space. Because the individual-machine potential energy is strictly zero in this angle surface, the constant- $\theta _{i}$ angle surface has a significant effect on the shape of the individual-machine potential energy surface. That is, the individual-machine potential energy surface is separated by a flat land, and mountains and valleys are located on either side of this flat land. In addition, a zero- $f_{i}$ angle surface also exists in the individual-machine potential energy surface. The individual-machine potential energy reaches a minimum or maximum at the surface. Using a scissor angle surface, the individual machine potential energy boundary that reflects the maximum individual-machine potential energy is obtained through the cut of the zero- $f_{i}$ angle surface. The machine becomes unstable after the system trajectory goes through the individual machine potential energy boundary. In the end, key concepts and distinctive phenomena in the individual-machine studies are fully explained using the concept of individual-machine potential energy surface.