1 (* chapter 'Biegelinie' from the textbook:
2 Timischl, Kaiser. Ingenieur-Mathematik 3. Wien 1999. p.268-271.
5 (c) due to copyright terms
7 remove_thy"Biegelinie";
8 use_thy"Knowledge/Biegelinie";
9 use_thy_only"Knowledge/Biegelinie";
11 remove_thy"Biegelinie";
12 use_thy"Knowledge/Isac";
15 Biegelinie = Integrate + Equation + EqSystem +
19 q_ :: real => real ("q'_") (* Streckenlast *)
20 Q :: real => real (* Querkraft *)
21 Q' :: real => real (* Ableitung der Querkraft *)
22 M'_b :: real => real ("M'_b") (* Biegemoment *)
23 M'_b' :: real => real ("M'_b'") (* Ableitung des Biegemoments *)
24 y'' :: real => real (* 2.Ableitung der Biegeline *)
25 y' :: real => real (* Neigung der Biegeline *)
26 (*y :: real => real (* Biegeline *)*)
27 EI :: real (* Biegesteifigkeit *)
29 (*new Descriptions in the related problems*)
30 Traegerlaenge :: real => una
31 Streckenlast :: real => una
32 BiegemomentVerlauf :: bool => una
33 Biegelinie :: (real => real) => una
34 Randbedingungen :: bool list => una
35 RandbedingungenBiegung :: bool list => una
36 RandbedingungenNeigung :: bool list => una
37 RandbedingungenMoment :: bool list => una
38 RandbedingungenQuerkraft :: bool list => una
39 FunktionsVariable :: real => una
40 Funktionen :: bool list => una
41 Gleichungen :: bool list => una
44 Biegelinie2Script :: "[real,real,real,real=>real,bool list,
46 ("((Script Biegelinie2Script (_ _ _ _ _ =))// (_))" 9)
47 BiegelinieScript :: "[real,real,real,real=>real,bool list,bool list,
49 ("((Script BiegelinieScript (_ _ _ _ _ _ =))// (_))" 9)
50 Biege2xIntegrierenScript :: "[real,real,real,bool,real=>real,bool list,
52 ("((Script Biege2xIntegrierenScript (_ _ _ _ _ _ =))// (_))" 9)
53 Biege4x4SystemScript :: "[real,real,real,real=>real,bool list,
55 ("((Script Biege4x4SystemScript (_ _ _ _ _ =))// (_))" 9)
56 Biege1xIntegrierenScript ::
57 "[real,real,real,real=>real,bool list,bool list,bool list,
59 ("((Script Biege1xIntegrierenScript (_ _ _ _ _ _ _ =))// (_))" 9)
60 Belastung2BiegelScript :: "[real,real,
61 bool list] => bool list"
62 ("((Script Belastung2BiegelScript (_ _ =))// (_))" 9)
63 SetzeRandbedScript :: "[bool list,bool list,
64 bool list] => bool list"
65 ("((Script SetzeRandbedScript (_ _ =))// (_))" 9)
69 Querkraft_Belastung "Q' x = -q_ x"
70 Belastung_Querkraft "-q_ x = Q' x"
72 Moment_Querkraft "M_b' x = Q x"
73 Querkraft_Moment "Q x = M_b' x"
75 Neigung_Moment "y'' x = -M_b x/ EI"
76 Moment_Neigung "M_b x = -EI * y'' x"
78 (*according to rls 'simplify_Integral': .. = 1/a * .. instead .. = ../ a*)
79 make_fun_explicit "Not (a =!= 0) ==> (a * (f x) = b) = (f x = 1/a * b)"