Patent ID: 11897635
Assignee: SPACE ENGINEERING UNIVERSITY
Field: Transport (Mechanical engineering)
Classification: CPC B  G | IPC B  G

Claim 9:
10. The method for maintaining Walker constellation formation according to claim 5, wherein the step of determining the first offset amount of each satellite according to the first-order variation rate and the variation acceleration further comprises:
determining the first offset amount of each satellite according to a fifth formula, which is written as:, {
  
   
    
     
      
       
        k
        1
        Ω
       
       =
       
        
         
          
           ∂
           
            Ω
            ˙
           
          
          
           ∂
           a
          
         
         ⁢
         Δ
         ⁢
         
          a
          0
         
        
        +
        
         
          
           ∂
           
            Ω
            ˙
           
          
          
           ∂
           e
          
         
         ⁢
         Δ
         ⁢
         
          e
          0
         
        
        +
        
         
          
           ∂
           
            Ω
            ˙
           
          
          
           ∂
           i
          
         
         ⁢
         Δ
         ⁢
         
          i
          0
         
        
       
      
     
    
    
     
      
       
        k
        1
        λ
       
       =
       
        
         
          
           ∂
           
            λ
            ˙
           
          
          
           ∂
           a
          
         
         ⁢
         Δ
         ⁢
         
          a
          0
         
        
        +
        
         
          
           ∂
           
            λ
            ˙
           
          
          
           ∂
           e
          
         
         ⁢
         Δ
         ⁢
         
          e
          0
         
        
        +
        
         
          
           ∂
           
            λ
            ˙
           
          
          
           ∂
           i
          
         
         ⁢
         Δ
         ⁢
         
          i
          0
         
        
       
      
     
    
    
     
      
       
        k
        2
        Ω
       
       =
       
        
         
          
           ∂
           
            Ω
            ˙
           
          
          
           ∂
           a
          
         
         ⁢
         Δ
         ⁢
         
          a
          ˙
         
        
        +
        
         
          
           ∂
           
            Ω
            ˙
           
          
          
           ∂
           e
          
         
         ⁢
          
         Δ
         ⁢
         
          e
          .
         
        
        +
        
         
          
           ∂
           
            Ω
            ˙
           
          
          
           ∂
           i
          
         
         ⁢
         Δ
         ⁢
         
          i
          ˙
         
        
       
      
     
    
    
     
      
       
        k
        2
        λ
       
       =
       
        
         
          
           ∂
           
            λ
            ˙
           
          
          
           ∂
           a
          
         
         ⁢
         Δ
         ⁢
         
          a
          ˙
         
        
        +
        
         
          
           ∂
           
            λ
            ˙
           
          
          
           ∂
           e
          
         
         ⁢
         Δ
         ⁢
         
          e
          ˙
         
        
        +
        
         
          
           ∂
           
            λ
            ˙
           
          
          
           ∂
           i
          
         
         ⁢
         Δ
         ⁢
         
          i
          ˙
         
        
       
      
     
    
   
   ,
  
 

where Δα0 is an offset amount of the nominal semi-major axis, Δe0 is an offset amount of an eccentricity, Δi0 is an offset amount of an orbit inclination,, ∂
    
     Ω
     ˙
    
   
   
    ∂
    a
   
  
  ,
  
   
    ∂
    
     Ω
     ˙
    
   
   
    ∂
    e
   
  
  ,
  
   
    ∂
    
     Ω
     ˙
    
   
   
    ∂
    i, are partial derivatives of a variation rate of a right ascension of ascending node influenced by a perturbative force with respect to the semi-major axis, the eccentricity and the orbit inclination, respectively,, ∂
    
     λ
     ˙
    
   
   
    ∂
    a
   
  
  ,
  
   
    ∂
    
     λ
     ˙
    
   
   
    ∂
    e
   
  
  ,
  
   
    ∂
    
     λ
     ˙
    
   
   
    ∂
    i, are partial derivatives of a variation rate of an along-track angle influenced by the perturbative force with respect to the semi-major axis, the eccentricity and the orbit inclination, respectively, and Δ{dot over (a)}, Δė, Δ{dot over (i)} are respective variation rates, which are determined by the perturbative forces applied to the respective satellite.