Simulation of the Radiation Reaction Orbits of a Classical Relativistic Charged Particle with Generalized Off-Shell Lorentz Force

Table 2

Second set. The parameters: 𝜇=3∗10⁵  GeV^-1 Hz, 𝑀/𝛼=4.84473∗10⁻¹⁰  GeV².

Initial conditions for the orbit		The third and forth derivatives (calculated with the initial
equation		conditions for the orbit equation)
𝑥̇0=1.001	𝑥̈0=1.6476	𝑥⃛0=22.5575	^.𝑥^...0=124.9841
𝑥̇1=0.1	𝑥̈1=4	𝑥⃛1=11.9631	^.𝑥^...1=58.5639
𝑥̇2=0.2	𝑥̈2=1	𝑥⃛2=6.2052	^.𝑥^...2=33.0308
𝑥̇3=0.3	𝑥̈3=2	𝑥⃛3=10.5736	^.𝑥^...3=55.5532
The orbit equation result
𝜀⃛=2⋅(𝑥̇𝑥𝜇^....𝜇+3𝑥̈𝜇𝑥⃛^𝜇)=36.272327445316
Initial conditions for the autonomous equation
𝜀=1−𝑥̇^20+𝑥̇^21+𝑥̇^22+𝑥̇^23=0.13800
𝜀̇=2⋅(−𝑥̇0⋅𝑥̈0+𝑥̇1⋅𝑥̈1+𝑥̇2⋅𝑥̈2+𝑥̇3⋅𝑥̈3)=−0.89850
𝜀̈=2⋅(−𝑥̇0⋅𝑥⃛0+𝑥̇1⋅𝑥⃛1+𝑥̇2⋅𝑥⃛2+𝑥̇3⋅𝑥⃛3−𝑥̈0⋅𝑥̈0+𝑥̈1⋅𝑥̈1+𝑥̈2⋅𝑥̈2+𝑥̈3⋅𝑥̈3)=2.62951
The autonomous equation result
𝜀⃛=36.272327445316