Fun With the HP 42S
Previous Links:
HP 42S Programming Part I: Matrix Column Sum, GCD, Error Function: http://edspi31415.blogspot.com/2016/07/hp-42s-programming-part-i-matrix-column.html
HP 42S Programming Part II: Dew Point, Ellipse Area and Eccentricity, Easy Transverse:
http://edspi31415.blogspot.com/2016/07/hp-42s-programming-part-ii-dew-point.html
HP 42S Programming Part III: Numerical Derivative, Recurring Sequences, Fractions:
http://edspi31415.blogspot.com/2016/07/hp-42s-programming-part-iii-numerical.html
Previous Links:
HP 42S Programming Part I: Matrix Column Sum, GCD, Error Function: http://edspi31415.blogspot.com/2016/07/hp-42s-programming-part-i-matrix-column.html
HP 42S Programming Part II: Dew Point, Ellipse Area and Eccentricity, Easy Transverse:
http://edspi31415.blogspot.com/2016/07/hp-42s-programming-part-ii-dew-point.html
HP 42S Programming Part III: Numerical Derivative, Recurring Sequences, Fractions:
http://edspi31415.blogspot.com/2016/07/hp-42s-programming-part-iii-numerical.html
HP 42S Julian
Date
Given month,
day, year, and university time (Greenwich), the Julian date is calculated. For January 1, 2000 at 12:00 AM, the date is
2,451,545.5.
00 {141-Byte
Prgm}
01 LBL
“JULDATE”
02 “MONTH”
03 PROMPT
04 STO 01
05 “DAY”
06 PROMPT
07 STO 02
08 “4 DIGIT
YEAR”
09 PROMPT
10 STO 03
11 “UT TIME”
12 PROMPT
13 STO 04
14 367
15 RCL* 03
16 STO 00
17 9
18 RCL+ 01
19 12
20 ÷
21 IP
22 RCL+ 03
23 4
24 ÷
25 7
26 *
27 IP
28 STO -00
29 RCL 01
30 9
31 –
32 7
33 ÷
34 RCL+ 03
35 100
36 ÷
37 IP
38 3
39 *
40 4
41 ÷
42 IP
43 STO- 00
44 275
45 RCL* 01
46 9
47 ÷
48 IP
49 STO+ 00
50 RCL 02
51 STO+ 00
52 1721028.5
53 STO+ 00
54 RCL 04
55 24
56 ÷
57 STO+ 00
58 RCL 00
59 END
Example:
Input: May 8, 2017, 03:00 UT. Result:
2457881.6250
HP
42S Sun Approximate Declination, Altitude, and Azimuth
Input: Days after the vernal equinox (typically
March 21), Earth’s latitude (north/south), number of hours after local noon
(example: for 7 AM, enter -5. For 7 PM, enter 7).
00
{ 147-Byte Prgm }
01
LBL “SUNAA”
02
DEG
03
“DAYS AFTER EQ.”
04
PROMPT
05
STO 00
06
“LATTITUDE”
07
PROMPT
08
STO 01
09
“HRS AFTER NOON”
10
PROMPT
11
STO 02
12
0.9856
13
RCL* 00
14
SIN
15
23.45
16
*
17
STO 04
18
COS
19
RCL 01
20
COS
21
*
22
15
23
RCL* 02
24
COS
25
*
26
RCL 01
27
SIN
28
RCL 04
29
SIN
30
*
31
+
32
ASIN
33
STO 05
34
SIN
35
RCL 01
36
SIN
37
*
38
RCL 04
39
SIN
40
–
41
RCL 05
42
COS
43
RCL 01
44
COS
45
*
46
÷
47
ACOS
48
STO 06
49
RCL 04
50
“DECLINATION”
51
AVIEW
52
STOP
53
RCL 05
54
“ALTITUDE”
55
AVIEW
56
STOP
57
RCL 06
58
“AZIMUTH”
59
AVIEW
60
END
Example:
Input: 100 days after the vernal equinox, 43.72° N,
about 12 noon (T = 0)
Results: Declination ≈ 23.1888°, Altitude: 69.4688°, Azimuth: 0.0002°
HP
42S Chebyshev Polynomial
The
trigonometric definition is used to calculate T_n(x):
For
|x| > 1, cosh (n * acosh x)
For
|x| ≤ 1, cos (n * acos x)
00
{42-Byte Prgm}
01
LBL “CHEBY”
02
“N”
03
PROMPT
04
STO 00
05
“X”
06
PROMPT
07
STO 01
08
ABS
09
1
10
X≥Y?
11
GTO 00
12
RCL 01
13
ACOSH
14
RCL* 00
15
COSH
16
GTO 01
17
LBL 00
18
RCL 01
19
ACOS
20
RCL* 00
21
COS
22
LBL 01
23
END
Examples:
T_4(2)
(n = 4, x = 2). Result: 97
T_4(0.5) (n = 4, x = 0.5) Result:
-0.5
HP
42S Pulley
There
are two weights in a pulley system, held by a rope has a negligible
contribution. The program uses SI units
(kg, m, s, with g = 9.80665 m/s^2). The
simultaneous equations solve for acceleration (m/s^2) and tensions:
T
– m1 * a = m1 * g
T
+ m2 * a = m2 * g
Source: HP 22S Science Student Applications. Edition 1.
Corvallis, Oregon. May 1988
00
{161-Byte Prgm}
01
LBL “PULLEY”
02
“MASS 1 (KG)”
03
PROMPT
04
STO 01
05
“MASS 2 (KG)”
06
PROMPT
07
STO 02
08
9.80665
09
STO 00
10
2
11
ENTER
12
2
13
DIM “MAT1”
14
INDEX “MAT1”
15
1
16
STOEL
17
J+
18
RCL 01
19
+/-
20
STOEL
21
2
22
ENTER
23
1
24
STOIJ
25
1
26
STOEL
27
J+
28
RCL 02
29
STOEL
30
2
31
ENTER
32
1
33
DIM “MAT2”
34
INDEX “MAT2”
35
RCL 00
36
RCL* 01
37
STOEL
38
I+
39
RCL 00
40
RCL* 02
41
STOEL
42
RCL “MAT1”
43
INVRT
44
RCL “MAT2”
45
*
46
STO “MAT3”
47
INDEX “MAT3”
48
RCLEL
49
“T”
50
AVIEW
51
STOP
52
I+
53
RCLEL
54
“a”
55
AVIEW
56
END
Example: m1 = 32 kg, m2 = 56 kg
Result: tension = 399.3981, a = 2.6745 m/s^2
HP
42S Rotation Matrix
R
= [[ cos θ, -sin θ ],[ sin θ, cos θ ]]
00
{138-Byte Prgm}
01
LBL “ROTATE2”
02
DEG
03
“ANGLE °”
04
PROMPT
05
STO 00
06
1
07
ENTER
08
2
09
DIM “MAT1”
10
INDEX “MAT1”
11
“X0”
12
PROMPT
13
STOEL
14
J+
15
“Y0”
16
PROMPT
17
STOEL
18
2
19
ENTER
20
2
21
DIM “MAT2”
22
INDEX “MAT2”
23
RCL 00
24
COS
25
STOEL
26
J+
27
RCL 00
28
SIN
29
+/-
30
STOEL
31
2
32
ENTER
33
1
34
STOIJ
35
RCL 00
36
SIN
37
STOEL
38
J+
39
RCL 00
40
COS
41
STOEL
42
RCL “MAT1”
43
RCL “MAT2”
44
*
45
STO “MAT3”
46
INDEX “MAT3”
47
RCLEL
48
“X1”
49
AVIEW
50
STOP
51
J+
52
RCLEL
53
“Y1”
54
AVIEW
55
END
Example:
Input: [3, -2], at an angle θ = 40°
Result: [ 1.0126, -3.4605 ]
Always fun working with the classic HP 42S!
Eddie
This blog is property of Edward Shore
