Search results for "Transformation equation"
showing 2 items of 2 documents
Action-Angle Variables
2001
In the following we will assume that the Hamiltonian does not depend explicitly on time; ∂H/∂t = 0. Then we know that the characteristic function W(q i , P i ) is the generator of a canonical transformation to new constant momenta P i , (all Q i , are ignorable), and the new Hamiltonian depends only on the P i ,: H = K = K(P i ). Besides, the following canonical equations are valid: $$ \dot Q_i = \frac{{\partial K}} {{\partial P_i }} = v_i = const. $$ (1) $$ \dot P_i = \frac{{\partial K}} {{\partial Q_i }} = 0. $$ (2)
The body-mind problem from a personality relativity theory approach: (Relativity of personality)
2012
The body-mind problem is here posed fromthe General Factor of Personality Theory and mathematically presented as a relativity theory: 1. A two-level-invariant model; 2. The transformation equation between both levels. On a hand, the investigation of personality dynamicsas a consequenceof a stimulant drug provides a system of two coupled differential equations, which adapts to both biological (body) and psychological (mind)levels ofdescription. On the other hand, a system of two coupled partial differential equations is here deduced as the transformation model between the biological and psychological levels. Both models are presented and validated in this paper. The experimental design to va…