(* chapter 'Biegelinie' from the textbook: 

   Timischl, Kaiser. Ingenieur-Mathematik 3. Wien 1999. p.268-271.

   author: Walther Neuper

   050826,

   (c) due to copyright terms

remove_thy"Biegelinie";

use_thy"Knowledge/Biegelinie";

use_thy_only"Knowledge/Biegelinie";

remove_thy"Biegelinie";

use_thy"Knowledge/Isac";

*)

Biegelinie = Integrate + Equation + EqSystem +

consts

  q_    :: real => real ("q'_")     (* Streckenlast               *)

  Q     :: real => real             (* Querkraft                  *)

  Q'    :: real => real             (* Ableitung der Querkraft    *)

  M'_b  :: real => real ("M'_b")    (* Biegemoment                *)

  M'_b' :: real => real ("M'_b'")   (* Ableitung des Biegemoments *)

  y''   :: real => real             (* 2.Ableitung der Biegeline  *)

  y'    :: real => real             (* Neigung der Biegeline      *)

(*y     :: real => real             (* Biegeline                  *)*)

  EI    :: real                     (* Biegesteifigkeit           *)

  (*new Descriptions in the related problems*)

  Traegerlaenge            :: real => una

  Streckenlast             :: real => una

  BiegemomentVerlauf       :: bool => una

  Biegelinie               :: (real => real) => una

  Randbedingungen          :: bool list => una

  RandbedingungenBiegung   :: bool list => una

  RandbedingungenNeigung   :: bool list => una

  RandbedingungenMoment    :: bool list => una

  RandbedingungenQuerkraft :: bool list => una

  FunktionsVariable        :: real => una

  Funktionen               :: bool list => una

  Gleichungen              :: bool list => una

  (*Script-names*)

  Biegelinie2Script        :: "[real,real,real,real=>real,bool list,

				bool] => bool"	

	("((Script Biegelinie2Script (_ _ _ _ _ =))// (_))" 9)

  BiegelinieScript         :: "[real,real,real,real=>real,bool list,bool list,

				bool] => bool"	

	("((Script BiegelinieScript (_ _ _ _ _ _ =))// (_))" 9)

  Biege2xIntegrierenScript :: "[real,real,real,bool,real=>real,bool list,

				bool] => bool"		

	("((Script Biege2xIntegrierenScript (_ _ _ _ _ _ =))// (_))" 9)

  Biege4x4SystemScript     :: "[real,real,real,real=>real,bool list,  

				bool] => bool"	

	("((Script Biege4x4SystemScript (_ _ _ _ _ =))// (_))" 9)

  Biege1xIntegrierenScript :: 

	            "[real,real,real,real=>real,bool list,bool list,bool list,

		      bool] => bool"	

	("((Script Biege1xIntegrierenScript (_ _ _ _ _ _ _ =))// (_))" 9)

  Belastung2BiegelScript   :: "[real,real,

	                        bool list] => bool list"	

	("((Script Belastung2BiegelScript (_ _ =))// (_))" 9)

  SetzeRandbedScript       :: "[bool list,bool list,

	                        bool list] => bool list"	

	("((Script SetzeRandbedScript (_ _ =))// (_))" 9)

rules

  Querkraft_Belastung   "Q' x = -q_ x"

  Belastung_Querkraft   "-q_ x = Q' x"

  Moment_Querkraft      "M_b' x = Q x"

  Querkraft_Moment      "Q x = M_b' x"

  Neigung_Moment        "y'' x = -M_b x/ EI"

  Moment_Neigung        "M_b x = -EI * y'' x"

  (*according to rls 'simplify_Integral': .. = 1/a * .. instead .. = ../ a*)

  make_fun_explicit     "Not (a =!= 0) ==> (a * (f x) = b) = (f x = 1/a * b)"

end