Sentence examples for angle variables from inspiring English sources

In resonant case, the averaged equations for n action variables and α combinations of angle variables are derived.

We first explore the forwarding structure of the spherical inverted pendulum model and then find a control law to stabilize the angle variables.

In Section 2, we introduce the action-angle variables to transform the system (1.1) into a perturbation of an integrable system, and then give some growth estimates on the corresponding action and angle variables functions.

By ((f_{0})) and the action and angle variables transformation (2.3), there exist constants (B>0, F>0), such that biglvert r'(t) bigrvert = bigglvert frac{yf t,x)}{omega } biggrvert leq Br(t)+F,quad forall rneq 0.

Now in the following, we will give some growth estimation properties with respect to the action and angle variables functions (r(t theta _{0},r_{0})) and (theta (t theta _{0},r_{0})).

According to the action and angle variables transformation (2.3), we see that there exists (gamma >0) such that (vert tan Delta theta vert leq frac{gamma d}{sqrt{2lambda r(t)}}) when (Delta theta rightarrow 0 ).

Mechanical and electrical parameters of the generator are estimated separately and the load angle variable is also estimated.

There are also issues of the choices of the independent variable time or an angle variable and the space in which the linearization is carried out.

Different geometrical patterns (regular, variable angle, variable density) for diagrid structures are explored, together with a fully non uniform diagrid-like pattern which mimics the principal stress trajectories on the building façade.

Based on an asymptotic analysis we show that the integro-differential equation for radiative transfer can be replaced by a set of differential equations which are independent of angle variable and easy to solve using standard numerical discretizations.

Choosing a cubic form for the dependence of R = r 2 on μ and then rotating the system using an angle variable, θ, gives rise to the bifurcation structure required, as shown in Fig. 1.