GS_program_Relax_(v0.5) -- Sage

[Ćelije u kojima je prvi redak %auto ne trebate izvoditi ( evaluate ); one se izvode „same” pri otvaranju radnoga lista. Međutim, ako radni list ponovno pokrenete—ne izlazeći iz njega—s Restart worksheet (u izborniku Action... ), i njih ćete morati izvesti.]

%auto
load (DATA + 'relax.sage')

Relaksacijski postupci

Ivan Belostenec: Gazophylacium seu Latino-Illyrcum onomatum aerarium (1740.)

Primjer 1.: Crossov postupak

Iz poglavlja Relaksacijski postupci u bilješkama s predavanja

(Okvir je prikazan na slici 28. na stranici 50.)

Oznake čvorova su za upis podataka u program izmijenjene:

U bilješkama	U kôdu
$0_1$	0
$0_2$	1
$0_3$	2
$1_1$	3
$1_2$	4
$1_2$	5
$2_2$	6
$2_3$	7

Koeficijenti krutosti elemenata i čvorova i razdjelni koeficijenti izračunani su na stranicama 51. i 52., a momenti upetosti na stranici 53.

Prvi dio postupka: rješavanje nepomičnoga sistema za zadana opterećenja:

(Slika 29. na stranici 50.)

# razdjelni koeficijenti:
distr_f = { (3, 0): 0.25, (3, 4): 0.75, (4, 3): 0.32, (4, 1): 0.20, (4, 5): 0.32, (4, 6): 0.16, (5, 4): 0.55, (5, 2): 0.18, (5, 7): 0.27, (6, 4): 0.40, (6, 7): 0.60, (7, 6): 0.60, (7, 5): 0.40 } 

# prijenosni koeficijent:
co_f = 1/2

# momenti upetosti: 
mom_fe = { (0, 3): 26.3, (3, 0): -26.3, (4, 5): 52.3, (5, 4): -52.3, (6, 7): 26.1, (7, 6): -26.1 }

init_all (distr_f, co_f, mom_fe)

distribution factors:
   (3, 0): 0.25
   (3, 4): 0.75
   (4, 1): 0.20
   (4, 3): 0.32
   (4, 5): 0.32
   (4, 6): 0.16
   (5, 2): 0.18
   (5, 4): 0.55
   (5, 7): 0.27
   (6, 4): 0.40
   (6, 7): 0.60
   (7, 5): 0.40
   (7, 6): 0.60

carry-over factors:
   (3, 0): 1/2
   (3, 4): 1/2
   (4, 1): 1/2
   (4, 3): 1/2
   (4, 5): 1/2
   (4, 6): 1/2
   (5, 2): 1/2
   (5, 4): 1/2
   (5, 7): 1/2
   (6, 4): 1/2
   (6, 7): 1/2
   (7, 5): 1/2
   (7, 6): 1/2

initial moment lists:
   (0, 3): [26.3]
   (1, 4): []
   (2, 5): []
   (3, 0): [-26.3]
   (3, 4): []
   (4, 1): []
   (4, 3): []
   (4, 5): [52.3]
   (4, 6): []
   (5, 2): []
   (5, 4): [-52.3]
   (5, 7): []
   (6, 4): []
   (6, 7): [26.1]
   (7, 5): []
   (7, 6): [-26.1]

initial residual moments:
   3:   -26.3
   4:   52.3
   5:   -52.3
   6:   26.1
   7:   -26.1

distribution factors:
   (3, 0): 0.25
   (3, 4): 0.75
   (4, 1): 0.20
   (4, 3): 0.32
   (4, 5): 0.32
   (4, 6): 0.16
   (5, 2): 0.18
   (5, 4): 0.55
   (5, 7): 0.27
   (6, 4): 0.40
   (6, 7): 0.60
   (7, 5): 0.40
   (7, 6): 0.60

carry-over factors:
   (3, 0): 1/2
   (3, 4): 1/2
   (4, 1): 1/2
   (4, 3): 1/2
   (4, 5): 1/2
   (4, 6): 1/2
   (5, 2): 1/2
   (5, 4): 1/2
   (5, 7): 1/2
   (6, 4): 1/2
   (6, 7): 1/2
   (7, 5): 1/2
   (7, 6): 1/2

initial moment lists:
   (0, 3): [26.3]
   (1, 4): []
   (2, 5): []
   (3, 0): [-26.3]
   (3, 4): []
   (4, 1): []
   (4, 3): []
   (4, 5): [52.3]
   (4, 6): []
   (5, 2): []
   (5, 4): [-52.3]
   (5, 7): []
   (6, 4): []
   (6, 7): [26.1]
   (7, 5): []
   (7, 6): [-26.1]

initial residual moments:
   3:   -26.3
   4:   52.3
   5:   -52.3
   6:   26.1
   7:   -26.1

@interact
def _relax_step ( nd = ('node: ', None) ) : 
    if nd != None :
        distribute_and_carry_over (nd)
        calc_residuals()

reset

Click to the left again to hide and once more to show the dynamic interactive window

nsteps

relax_order

[4, 5, 3, 4, 6, 7, 6, 4, 3, 7, 4, 5, 6, 4, 7, 5, 4, 6, 3]

[4, 5, 3, 4, 6, 7, 6, 4, 3, 7, 4, 5, 6, 4, 7, 5, 4, 6, 3]

print_dict (moment_lists)

(0, 3): [26.3, 4.4, 0.50, 0.00]
(1, 4): [-5.2, -2.9, 0.50, -0.20, 0.00, 0.00]
(2, 5): [5.5, -0.10, 0.00]
(3, 0): [-26.3, 8.7, '|', 1.0, '|', 0.00, '|']
(3, 4): [-8.4, 26.0, '|', -4.8, 0.90, 2.9, '|', -0.20, 0.10, 0.00, 0.10, '|']
(4, 1): [-10.5, '|', -5.9, '|', 1.1, '|', -0.30, '|', 0.10, '|', 0.00, '|']
(4, 3): [-16.7, '|', 13.0, -9.5, '|', 1.7, '|', 1.5, -0.50, '|', 0.20, '|',
0.00, '|', 0.00]
(4, 5): [52.3, -16.7, '|', 16.6, -9.5, '|', 1.7, '|', -0.50, '|', -0.30, 0.20,
'|', -0.10, 0.00, '|']
(4, 6): [-8.4, '|', -4.7, '|', -3.9, -1.4, 0.80, '|', -0.20, '|', -0.20, 0.10,
'|', 0.00, '|', 0.00]
(5, 2): [10.9, '|', -0.20, '|', 0.00, '|']
(5, 4): [-52.3, -8.3, 33.3, '|', -4.7, 0.80, -0.30, -0.50, '|', 0.10, -0.10,
'|', 0.00]
(5, 7): [16.4, '|', 4.8, 0.40, -0.30, '|', 0.10, 0.00, '|']
(6, 4): [-4.2, -2.4, -7.8, '|', -2.8, '|', 0.40, -0.10, -0.40, '|', 0.00, 0.00,
0.00, '|']
(6, 7): [26.1, -11.7, '|', 7.1, -4.3, '|', 0.60, -0.50, '|', 0.10, -0.10, '|']
(7, 5): [8.2, 9.5, '|', 0.80, '|', -0.10, 0.20, '|', 0.00]
(7, 6): [-26.1, -5.8, 14.2, '|', -2.1, 1.3, '|', -0.30, 0.20, '|', 0.00]

(0, 3): [26.3, 4.4, 0.50, 0.00]
(1, 4): [-5.2, -2.9, 0.50, -0.20, 0.00, 0.00]
(2, 5): [5.5, -0.10, 0.00]
(3, 0): [-26.3, 8.7, '|', 1.0, '|', 0.00, '|']
(3, 4): [-8.4, 26.0, '|', -4.8, 0.90, 2.9, '|', -0.20, 0.10, 0.00, 0.10, '|']
(4, 1): [-10.5, '|', -5.9, '|', 1.1, '|', -0.30, '|', 0.10, '|', 0.00, '|']
(4, 3): [-16.7, '|', 13.0, -9.5, '|', 1.7, '|', 1.5, -0.50, '|', 0.20, '|', 0.00, '|', 0.00]
(4, 5): [52.3, -16.7, '|', 16.6, -9.5, '|', 1.7, '|', -0.50, '|', -0.30, 0.20, '|', -0.10, 0.00, '|']
(4, 6): [-8.4, '|', -4.7, '|', -3.9, -1.4, 0.80, '|', -0.20, '|', -0.20, 0.10, '|', 0.00, '|', 0.00]
(5, 2): [10.9, '|', -0.20, '|', 0.00, '|']
(5, 4): [-52.3, -8.3, 33.3, '|', -4.7, 0.80, -0.30, -0.50, '|', 0.10, -0.10, '|', 0.00]
(5, 7): [16.4, '|', 4.8, 0.40, -0.30, '|', 0.10, 0.00, '|']
(6, 4): [-4.2, -2.4, -7.8, '|', -2.8, '|', 0.40, -0.10, -0.40, '|', 0.00, 0.00, 0.00, '|']
(6, 7): [26.1, -11.7, '|', 7.1, -4.3, '|', 0.60, -0.50, '|', 0.10, -0.10, '|']
(7, 5): [8.2, 9.5, '|', 0.80, '|', -0.10, 0.20, '|', 0.00]
(7, 6): [-26.1, -5.8, 14.2, '|', -2.1, 1.3, '|', -0.30, 0.20, '|', 0.00]

sum_end_moments()

final moments:
   (0, 3): 31.2
   (1, 4): -7.8
   (2, 5): 5.4
   (3, 0): -16.6
   (3, 4): 16.6
   (4, 1): -15.5
   (4, 3): -10.3
   (4, 5): 43.7
   (4, 6): -17.9
   (5, 2): 10.7
   (5, 4): -32.0
   (5, 7): 21.4
   (6, 4): -17.3
   (6, 7): 17.3
   (7, 5): 18.6
   (7, 6): -18.6

final residual moments:
   3:   0.00
   4:   0.00
   5:   0.10
   6:   0.00
   7:   0.00

final moments:
   (0, 3): 31.2
   (1, 4): -7.8
   (2, 5): 5.4
   (3, 0): -16.6
   (3, 4): 16.6
   (4, 1): -15.5
   (4, 3): -10.3
   (4, 5): 43.7
   (4, 6): -17.9
   (5, 2): 10.7
   (5, 4): -32.0
   (5, 7): 21.4
   (6, 4): -17.3
   (6, 7): 17.3
   (7, 5): 18.6
   (7, 6): -18.6

final residual moments:
   3:   0.00
   4:   0.00
   5:   0.10
   6:   0.00
   7:   0.00

patch_moments()

final final moments:
   (0, 3): 31.2
   (1, 4): -7.8
   (2, 5): 5.4
   (3, 0): -16.6
   (3, 4): 16.6
   (4, 1): -15.5
   (4, 3): -10.3
   (4, 5): 43.7
   (4, 6): -17.9
   (5, 2): 10.7
   (5, 4): -32.1
   (5, 7): 21.4
   (6, 4): -17.3
   (6, 7): 17.3
   (7, 5): 18.6
   (7, 6): -18.6

final final moments:
   (0, 3): 31.2
   (1, 4): -7.8
   (2, 5): 5.4
   (3, 0): -16.6
   (3, 4): 16.6
   (4, 1): -15.5
   (4, 3): -10.3
   (4, 5): 43.7
   (4, 6): -17.9
   (5, 2): 10.7
   (5, 4): -32.1
   (5, 7): 21.4
   (6, 4): -17.3
   (6, 7): 17.3
   (7, 5): 18.6
   (7, 6): -18.6

Primjer 2.: Crossov postupak

Primjer u predavanju 6.

$q = 20 \mathrm{kN/m'},\qquad P = 75 \mathrm {kN}$

Prvi dio postupka: rješavanje nepomičnoga sistema za zadana opterećenja:

# razdjelni koeficijenti:
df = { (3, 1): 0.24, (3, 4): 0.47, (3, 5): 0.29, (4, 3): 0.44, (4, 2): 0.20, (4, 6): 0.36, (6, 4): 0.52, (6, 5): 0.48 }

# prijenosni koeficijenti:
cof = { (3, 1): 1/2, (3, 4): 1/2, (3, 5): 0, (4, 3): 1/2, (4, 2): 0, (4, 6): 1/2, (6, 4): 1/2, (6, 5): 0 }

# momenti upetosti:
fem = { (6, 5): -62.5, (4, 6): 16.7, (6, 4): -33.3 }

init_all (df, cof, fem)

distribution factors:
   (3, 1): 0.24
   (3, 4): 0.47
   (3, 5): 0.29
   (4, 2): 0.20
   (4, 3): 0.44
   (4, 6): 0.36
   (6, 4): 0.52
   (6, 5): 0.48

carry-over factors:
   (3, 1): 1/2
   (3, 4): 1/2
   (3, 5): 0
   (4, 2): 0
   (4, 3): 1/2
   (4, 6): 1/2
   (6, 4): 1/2
   (6, 5): 0

initial moment lists:
   (1, 3): []
   (2, 4): []
   (3, 1): []
   (3, 4): []
   (3, 5): []
   (4, 2): []
   (4, 3): []
   (4, 6): [16.7]
   (5, 3): []
   (5, 6): []
   (6, 4): [-33.3]
   (6, 5): [-62.5]

initial residual moments:
   3:   0.00
   4:   16.7
   6:   -95.8

distribution factors:
   (3, 1): 0.24
   (3, 4): 0.47
   (3, 5): 0.29
   (4, 2): 0.20
   (4, 3): 0.44
   (4, 6): 0.36
   (6, 4): 0.52
   (6, 5): 0.48

carry-over factors:
   (3, 1): 1/2
   (3, 4): 1/2
   (3, 5): 0
   (4, 2): 0
   (4, 3): 1/2
   (4, 6): 1/2
   (6, 4): 1/2
   (6, 5): 0

initial moment lists:
   (1, 3): []
   (2, 4): []
   (3, 1): []
   (3, 4): []
   (3, 5): []
   (4, 2): []
   (4, 3): []
   (4, 6): [16.7]
   (5, 3): []
   (5, 6): []
   (6, 4): [-33.3]
   (6, 5): [-62.5]

initial residual moments:
   3:   0.00
   4:   16.7
   6:   -95.8

@interact
def _relax_step ( nd = ('node: ', None) ) : 
    if nd != None :
        distribute_and_carry_over (nd)
        calc_residuals()

reset

Click to the left again to hide and once more to show the dynamic interactive window

nsteps

relax_order

[6, 4, 3, 6, 4, 3, 6, 4, 3]

[6, 4, 3, 6, 4, 3, 6, 4, 3]

print_dict (moment_lists)

(1, 3): [1.1, 0.10, 0.00]
(2, 4): [0.00, 0.00, 0.00]
(3, 1): [2.2, '|', 0.20, '|', 0.00, '|']
(3, 4): [-9.1, 4.3, '|', -0.90, 0.40, '|', -0.10, 0.00, '|']
(3, 5): [2.6, '|', 0.30, '|', 0.00, '|']
(4, 2): [-8.3, '|', -0.80, '|', -0.10, '|']
(4, 3): [-18.3, '|', 2.2, -1.8, '|', 0.20, -0.20, '|', 0.00]
(4, 6): [16.7, 24.9, -15.0, '|', 1.9, -1.5, '|', 0.20, -0.10, '|']
(5, 3): [0.00, 0.00, 0.00]
(5, 6): [0.00, 0.00, 0.00]
(6, 4): [-33.3, 49.8, '|', -7.5, 3.9, '|', -0.80, 0.40, '|', 0.00]
(6, 5): [-62.5, 46.0, '|', 3.6, '|', 0.40, '|']

(1, 3): [1.1, 0.10, 0.00]
(2, 4): [0.00, 0.00, 0.00]
(3, 1): [2.2, '|', 0.20, '|', 0.00, '|']
(3, 4): [-9.1, 4.3, '|', -0.90, 0.40, '|', -0.10, 0.00, '|']
(3, 5): [2.6, '|', 0.30, '|', 0.00, '|']
(4, 2): [-8.3, '|', -0.80, '|', -0.10, '|']
(4, 3): [-18.3, '|', 2.2, -1.8, '|', 0.20, -0.20, '|', 0.00]
(4, 6): [16.7, 24.9, -15.0, '|', 1.9, -1.5, '|', 0.20, -0.10, '|']
(5, 3): [0.00, 0.00, 0.00]
(5, 6): [0.00, 0.00, 0.00]
(6, 4): [-33.3, 49.8, '|', -7.5, 3.9, '|', -0.80, 0.40, '|', 0.00]
(6, 5): [-62.5, 46.0, '|', 3.6, '|', 0.40, '|']

sum_end_moments()

final moments:
   (1, 3): 1.2
   (2, 4): 0.00
   (3, 1): 2.4
   (3, 4): -5.4
   (3, 5): 2.9
   (4, 2): -9.2
   (4, 3): -17.9
   (4, 6): 27.1
   (5, 3): 0.00
   (5, 6): 0.00
   (6, 4): 12.5
   (6, 5): -12.5

final residual moments:
   3:   -0.10
   4:   0.00
   6:   0.00

final moments:
   (1, 3): 1.2
   (2, 4): 0.00
   (3, 1): 2.4
   (3, 4): -5.4
   (3, 5): 2.9
   (4, 2): -9.2
   (4, 3): -17.9
   (4, 6): 27.1
   (5, 3): 0.00
   (5, 6): 0.00
   (6, 4): 12.5
   (6, 5): -12.5

final residual moments:
   3:   -0.10
   4:   0.00
   6:   0.00

patch_moments()

final final moments:
   (1, 3): 1.2
   (2, 4): 0.00
   (3, 1): 2.4
   (3, 4): -5.3
   (3, 5): 2.9
   (4, 2): -9.2
   (4, 3): -17.9
   (4, 6): 27.1
   (5, 3): 0.00
   (5, 6): 0.00
   (6, 4): 12.5
   (6, 5): -12.5

final final moments:
   (1, 3): 1.2
   (2, 4): 0.00
   (3, 1): 2.4
   (3, 4): -5.3
   (3, 5): 2.9
   (4, 2): -9.2
   (4, 3): -17.9
   (4, 6): 27.1
   (5, 3): 0.00
   (5, 6): 0.00
   (6, 4): 12.5
   (6, 5): -12.5

Primjer 3.: Postupak Wernera i Csonke

Iz poglavlja Relaksacijski postupci u bilješkama s predavanja — nastavak Primjera 1.

(Poluokvir je prikazan lijevo na slici 43. na stranici 67.)

Oznake su čvorova za upis podataka:

čvorovi 0, 1, 2 su kao u bilješkama,
čvor 3 je pomični zglobni ležaj u razini čvora 1,
čvor 4 je pomični zglobni ležaj u razini čvora 2.

Koeficijenti krutosti greda, stupova i čvorova i razdjelni koeficijenti izračunani su na stranici 68., a momenti upetosti na stranici 69.

# razdjelni koeficijenti:
cw_distr_f = { (1, 0): 0.05, (1, 2): 0.04, (1, 3): 0.91, (2, 1): 0.10, (2, 4): 0.90 } 

# prijenosni koeficijenti: 
cw_co_f = { (1, 0): -1, (1, 2): -1, (1, 3): 0, (2, 1): -1, (2, 4): 0 } 

# momenti upetosti:
cw_mom_fe = { (0, 1): 153.9, (1, 0): 153.9, (1, 2): 67.6, (2, 1): 67.6 }

init_all (cw_distr_f, cw_co_f, cw_mom_fe)

distribution factors:
   (1, 0): 0.050
   (1, 2): 0.040
   (1, 3): 0.91
   (2, 1): 0.10
   (2, 4): 0.90

carry-over factors:
   (1, 0): -1
   (1, 2): -1
   (1, 3): 0
   (2, 1): -1
   (2, 4): 0

initial moment lists:
   (0, 1): [153.9]
   (1, 0): [153.9]
   (1, 2): [67.6]
   (1, 3): []
   (2, 1): [67.6]
   (2, 4): []
   (3, 1): []
   (4, 2): []

initial residual moments:
   1:   221.5
   2:   67.6

distribution factors:
   (1, 0): 0.050
   (1, 2): 0.040
   (1, 3): 0.91
   (2, 1): 0.10
   (2, 4): 0.90

carry-over factors:
   (1, 0): -1
   (1, 2): -1
   (1, 3): 0
   (2, 1): -1
   (2, 4): 0

initial moment lists:
   (0, 1): [153.9]
   (1, 0): [153.9]
   (1, 2): [67.6]
   (1, 3): []
   (2, 1): [67.6]
   (2, 4): []
   (3, 1): []
   (4, 2): []

initial residual moments:
   1:   221.5
   2:   67.6

@interact
def _relax_step ( nd = ('node: ', None) ) : 
    if nd != None :
        distribute_and_carry_over (nd)
        calc_residuals()

reset

Click to the left again to hide and once more to show the dynamic interactive window

nsteps

relax_order

[1, 2, 1, 2]

[1, 2, 1, 2]

sum_end_moments()

final moments:
   (0, 1): 165.4
   (1, 0): 142.4
   (1, 2): 66.0
   (1, 3): -208.5
   (2, 1): 69.2
   (2, 4): -69.2
   (3, 1): 0.00
   (4, 2): 0.00

final residual moments:
   1:   -0.10
   2:   0.00

final moments:
   (0, 1): 165.4
   (1, 0): 142.4
   (1, 2): 66.0
   (1, 3): -208.5
   (2, 1): 69.2
   (2, 4): -69.2
   (3, 1): 0.00
   (4, 2): 0.00

final residual moments:
   1:   -0.10
   2:   0.00

patch_moments()

final final moments:
   (0, 1): 165.4
   (1, 0): 142.4
   (1, 2): 66.0
   (1, 3): -208.4
   (2, 1): 69.2
   (2, 4): -69.2
   (3, 1): 0.00
   (4, 2): 0.00

final final moments:
   (0, 1): 165.4
   (1, 0): 142.4
   (1, 2): 66.0
   (1, 3): -208.4
   (2, 1): 69.2
   (2, 4): -69.2
   (3, 1): 0.00
   (4, 2): 0.00

print_dict (moment_lists)

(0, 1): [153.9, 11.1, 0.40]
(1, 0): [153.9, -11.1, '|', -0.40, '|']
(1, 2): [67.6, -8.9, '|', 7.6, -0.30, '|', 0.00]
(1, 3): [-201.6, '|', -6.9, '|']
(2, 1): [67.6, 8.9, -7.6, '|', 0.30, 0.00, '|']
(2, 4): [-68.9, '|', -0.30, '|']
(3, 1): [0.00, 0.00]
(4, 2): [0.00, 0.00]

(0, 1): [153.9, 11.1, 0.40]
(1, 0): [153.9, -11.1, '|', -0.40, '|']
(1, 2): [67.6, -8.9, '|', 7.6, -0.30, '|', 0.00]
(1, 3): [-201.6, '|', -6.9, '|']
(2, 1): [67.6, 8.9, -7.6, '|', 0.30, 0.00, '|']
(2, 4): [-68.9, '|', -0.30, '|']
(3, 1): [0.00, 0.00]
(4, 2): [0.00, 0.00]

Podsjetnik: rješavanje sustava linearnih jednadžbi

Sustav iz primjera u predavanju 6.

$47,\!9\, \varrho_1 \,-\, 23,\!1\, \varrho_2 \,-\, 147,\!8 \:=\: 0$

$-23,\!2\, \varrho_1 \,+\, 29,\!8\, \varrho_2 \,-\, 37,\!5 \:=\: 0$

var ('r1 r2')

(r1, r2)

(r1, r2)

r = solve ([47.9 * r1 - 23.1 * r2 - 147.8 == 0, 
            -23.2 * r1 + 29.8 * r2 - 37.5 == 0],
           [r1, r2])
show (r)

$\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left[r_{1} = \left(\frac{527069}{89150}\right), r_{2} = \left(\frac{522521}{89150}\right)\right]\right]$

N (r[0][0].rhs()), N (r[0][1].rhs())

(5.91215928210881, 5.86114413909142)

(5.91215928210881, 5.86114413909142)

NDP(2) (RR (r[0][0].rhs())), NDP(2) (RR (r[0][1].rhs()))

(5.91, 5.86)

(5.91, 5.86)

ili:

A = matrix ([[47.9, -23.1],
             [-23.2, 29.8]])

b = vector ([147.8, 37.5])

r = A \ b
r

(5.91215928210881, 5.86114413909142)

(5.91215928210881, 5.86114413909142)

NDP(2) (r[0]), NDP(2) (r[1])

(5.91, 5.86)

(5.91, 5.86)

map (NDP(2), r)

[5.91, 5.86]

[5.91, 5.86]

GS_program_Relax_(v0.5)

938 days ago by fresl

Click to the left again to hide and once more to show the dynamic interactive window

Click to the left again to hide and once more to show the dynamic interactive window

Click to the left again to hide and once more to show the dynamic interactive window