Impulse-Momentum Diagrams

Angular Momentum Diagrams

Starting from the simplest possible building blocks—a ket, a bra, a time-reversed ket, and a time-reversed bra— a diagrammatic formalism is developed for angular momentum coupling problems. The formalism comprises Clebsch–Gordan coefficients as well as 3jm-symbols. The idea of constructing invariants (internal lines) by contracting contragredient pairs of quantities is emphasized throughout. Th...

Gait consistency test based on the impulse-momentum theorem.

Swing-Up Control of the Pendubot: An Impulse-Momentum Approach

The standard control problem of the pendubot refers to the task of stabilizing its equilibrium configuration with the highest potential energy. Linearization of the dynamics of the pendubot about this equilibrium results in a completely controllable system and allows a linear controller to be designed for local asymptotic stability. For the underactuated pendubot, the important task is, therefo...

Momentum Distributions and the Impulse Approximation in Helium

The momentum distribution n(p) of atoms in condensed matter may be determined from neutron inelastic scattering measurements. However, scattering at high momentum transfers hQ (high enough that the impulse approximation holds) is required. A model of solid helium is used to assess the error introduced in n(p) by assuming the impulse approximation holds at several Q values. At Q=2Ofi -1 the erro...

4 Diagrams in Momentum Space 4.1 Fourier Transformation

At the end of Section 2.3, we have observed that all correlation functions of the local field theory under consideration are invariant under spatial translations. This invariance has the consequence that Feynman integrals are greatly simplified by Fourier transformation. It is therefore useful to set up rules for composing Feynman integrals directly in momentum space.