So for slight displacement, the restoring force should act on the body Now For equilibrium, Force should be zeroįor stable equilibrium, the second derivative should be positive. If only conservative forces are acting on the system, then we can define equilibrium in terms of Potential energy also If no force acting then neutral equilibrium if the force is away i,e direction is away from the equilibrium position then it is an unstable equilibrium.
If the force is restoring i,e direction is towards the equilibrium position then it is a stable equilibrium. (3) We will need to find the direction of the force on the body when slightly displaced to find out if the equilibrium is stable, unstable, or neutral. This looks to be very clear from the example ball in the valley if the center of gravity is tilted below on displacement from the equilibrium position, then the body will not come back to the normal position. So if the center of gravity is tilted above on displacement from the equilibrium position, then the body will come back to the lowest point. (2) The body always tries to go to the lowest point for the center of gravity. The higher it is the more likely the object is to topple over if it is pushed. The lower the center of gravity (G) is, the more stable the object. (1) The position of the center of gravity of an object affects its stability. (4) A ball at the top of a rounded hill.A small displacement of the ball results in a force that moves the ball away from the equilibrium point so that equilibrium cannot be maintained. (2) thin rod standing vertically is slightly disturbed from its position it will not come back to its original position. (1) pencil standing on its point or a stick in vertically standing position. Unstable equilibrium: A body is in unstable equilibrium if it does comes back to its normal position on slight displacement A small displacement will not have any impact on the ball. Neutral equilibrium: If a ball is pushed slightly to roll, it will neither come back to its original nor it will roll forward rather it will remain at rest. If the clone is tilted slightly, it comes back to its normal position (3) A cone with a flat surface on the horizontal floor. If the book is lifted from one edge and then allowed to fall, it will come back to its original position (2)A book lying on a horizontal surface is an example of stable equilibrium. a small displacement of the ball toward either side will result in a force returning the ball to the original position. (1) A ball in the valley between two hills. It is applied to calculate non-axisymmetric, toroidal equilibria with one or more magnetic axes and to determine the instabilities of helical l = 2 and 3 configurations.Stable Equilibrium: A body is in stable equilibrium if it comes back to its normal position on slight displacement
Stable equilibrium 3d code#
The code is checked against known analytical results and the dependence on the mesh size is studied. By this choice numerical flux conservation is not automatically guaranteed but it is possible to handle complicated field topologies. The computation grid is Eulerian corresponding to space-fixed cylindrical coordinates whose boundary is a torus surface with rectangular cross section. Time integration of this method is explicit with time steps of varying length which admits a mean step two orders of magnitude larger than the usual stability limit. A third method (MHF) introduces an artificial time and derives additional information on the lowest eigenvalue of the asymptotic linear problem from time history. As minimizing algorithms we used the gradient and conjugate gradient methods which are modified such that their convergence rate was greatly improved. A code is described which transfers an arbitrary initial plasma and field configuration under the constraints of mass and flux conservation into an equilibrium state by minimizing the energy of the system so that, in principle, the equilibrium attained is stable.
0 kommentar(er)
