Chapter 6, Section 6.10.2

Here we are going to derive an explicit expression for one resonant term associated with the motion of Pallas close to the 18:7 resonance with Jupiter.

We start by loading the DisturbingFunction package.  In this example it is assumed that the file DisturbingFunction.m is located in the current directory/folder.

<<DisturbingFunction.m;

Show how the function ValidArguments is used.

?ValidArguments

Use ValidArguments to find all the resonant arguments (associated with terms up to eleventh order in the eccentricities and inclinations) of a form 18λ'–7λ+ ... .

args187 = ValidArguments[18,-7,11]

Tere are 182 such arguments.

Length[args187]

The one we have chosen (arbitrarily) is the thirty-first.

argument=args187[[31]]

Show how the function DisturbingFunctionE is used.

?DisturbingFunctionE

Use DisturbingFunctionE to find the terms (to eleventh order) associated with this argument.

resonant = DisturbingFunctionE[argument,11]

Isolate the dimensionless terms in which we are interested (see Eq.(6.217)).

Expand[resonant*12288/𝒢/m'*a']