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Differential Equation of a Central Orbit - Polar Form
Lesson 61 of 135 • 3 upvotes • 5:26mins
Asim Anand
Polar form.
Mathematics Optional for UPSC - Dynamics
135 lessons • 9h 47m
1
Overview
1:42mins
2
Kinematics in Two Dimensions - I [Chapter 1]
10:33mins
3
Kinematics in Two Dimensions - II
9:50mins
4
Kinematics in Two Dimensions - III
10:56mins
5
Kinematics in Two Dimensions - IV
8:45mins
6
Solved Examples - I
9:52mins
7
Solved Examples - II
11:19mins
8
Solved Examples - III
12:40mins
9
Radial and Transverse Velocities
4:53mins
10
Radial and Transverse Accelerations
2:35mins
11
Solved Examples
4:30mins
12
Tangential and Normal Velocities
6:24mins
13
Tangential and Normal Accelerations
3:17mins
14
Solved Examples [Chapter 1 conclusion]
2:43mins
15
Rectilinear Motion - Introduction [Chapter 2]
6:32mins
16
Solved Examples
6:12mins
17
Motion under Constant Acceleration
4:12mins
18
Solved Examples
9:51mins
19
Newton's Laws of Motion
3:14mins
20
Simple Harmonic Motion (S.H.M.) - Introduction
10:29mins
21
S.H.M. - Nature of motion
4:33mins
22
S.H.M. - Important Definitions
9:26mins
23
Geometrical Representation of S.H.M.
5:23mins
24
Important results about S.H.M.
2:17mins
25
Solved Examples
13:24mins
26
Hooke's Law
5:11mins
27
Horizontal Elastic String - Equations of Motion
5:32mins
28
Horizontal Elastic String - Character of Motion
6:09mins
29
Solved Example
6:59mins
30
Vertical Elastic String - Equations of Motion
7:10mins
31
Vertical Elastic String - Two important cases
7:27mins
32
Solved Examples
11:24mins
33
Correction
0:32mins
34
Motion under Inverse Square Law
7:53mins
35
Newton's Law of Gravitation
1:25mins
36
Solved Examples
9:49mins
37
Motion under Miscellaneous Laws of Forces [Chapter 2 conclusion]
7:22mins
38
Constrained Motion - Motion in a Vertical Circle [Chapter 3]
11:09mins
39
Motion in a Vertical Circle - Case I
1:59mins
40
Motion in a Vertical Circle - Case II
1:21mins
41
Motion in a Vertical Circle - Case III
2:47mins
42
Motion in a Vertical Circle - Case IV
3:32mins
43
Important Results from Projectiles
3:59mins
44
Solved Examples
5:38mins
45
Motion on the Outside of a smooth Vertical Circle
10:30mins
46
Solved Examples
6:28mins
47
Cycloid
4:37mins
48
Motion on a Cycloid - I
5:44mins
49
Motion on a Cycloid - II
3:33mins
50
Solved Examples
4:44mins
51
Motion on the outside of a smooth Cycloid
5:25mins
52
Solved Examples
14:31mins
53
Simple Pendulum - Introduction
2:40mins
54
Simple Pendulum - Small Oscillations
1:10mins
55
Simple Pendulum - Oscillations are not small
5:24mins
56
Beats and Second's Pendulum
2:35mins
57
Gain or Loss of Beats
4:41mins
58
Gain or loss of beats - Specific Situations
4:18mins
59
Solved Example [Chapter 3 conclusion]
2:14mins
60
Central Orbits - Introduction [Chapter 4]
5:56mins
61
Differential Equation of a Central Orbit - Polar Form
5:26mins
62
Differential Equation of a Central Orbit - Pedal Form
4:37mins
63
Rate of Description of the Sectorial Area
8:51mins
64
Elliptic Orbit - Law of Force
3:16mins
65
Elliptic Orbit - Velocity at any point
2:12mins
66
Elliptic Orbit - Periodic Time
2:37mins
67
Hyperbolic & Parabolic Orbits
2:05mins
68
Velocity from Infinity
2:45mins
69
Velocity in a Circle
2:31mins
70
Given the Central Orbit, to find the Law of Force
2:27mins
71
Solved Examples
6:56mins
72
Apse, Apsidal Distance & Apsidal Angle
3:15mins
73
Theorem
3:03mins
74
Given the Law of Force, to find the Orbit
1:29mins
75
Solved Examples [Chapter 4 conclusion]
10:55mins
76
Planetary Motion - Newton's Law of Gravitation [Chapter 5]
1:27mins
77
Motion under the Inverse Square Law
3:29mins
78
Elliptic, Parabolic & Hyperbolic Paths
2:18mins
79
Summary of the three cases
4:49mins
81
Kepler's Laws of Planetary Motion
0:52mins
82
Deductions from Kepler's Laws
2:28mins
83
Important Geometrical Properties of an Ellipse
2:42mins
84
Solved Examples
9:55mins
85
Time of description of an arc - Parabolic Orbit
3:30mins
86
Time of description of an arc - Elliptic Orbit
5:11mins
87
Time of description of an arc - Hyperbolic Orbit [Chapter 5 conclusion]
3:59mins
88
Motion in a Resisting Medium - Introduction [Chapter 6]
1:43mins
89
Terminal Velocity
2:14mins
90
Motion of a Particle falling under Gravity - Relation between v & x
4:25mins
91
Motion of a Particle falling under Gravity - Relation between v & t
2:14mins
92
Motion of a Particle falling under Gravity - Relation between x & t
1:16mins
93
Motion of a Particle Projected Vertically Upwards
5:41mins
94
Solved Examples [Chapter 6 conclusion]
6:10mins
95
Projectile Motion - Introduction [Chapter 7]
1:05mins
96
Motion of a Projectile & it's Trajectory - I
5:32mins
97
Motion of a Projectile and it's Trajectory - II
2:04mins
98
Latus Rectum of the Trajectory
2:45mins
99
Vertex & Focus of the Trajectory
3:29mins
100
Directrix of the Trajectory
1:30mins
101
Time of Flight
1:43mins
102
Horizontal Range
0:57mins
103
Maximum Horizontal Range
3:29mins
104
Maximum Height
0:59mins
105
Velocity at any point of the Trajectory
3:10mins
106
Locus of the Focus of the Trajectory
1:55mins
107
Locus of the Vertex of the Trajectory
1:22mins
108
Important Geometrical Properties of a Parabola
2:11mins
109
Solved Examples
5:40mins
110
Two directions of projection to hit a given point
1:38mins
111
Least velocity of projection to hit a given point
2:30mins
112
Two times of flight to hit a given point
2:13mins
113
Range and Time of Flight on an Inclined Plane
5:20mins
114
Maximum Range up the Inclined Plane
5:14mins
115
Range & Time of Flight down an Inclined Plane
5:16mins
116
Solved Examples
4:29mins
117
Envelope of the Trajectories with the same Velocity of Projection
5:17mins
118
Geometrical Interpretation of the Enveloping Parabola & Solved Example
5:21mins
119
Particles suffered to describe Parabolic Paths & Solved Example [Chapter 7 conclusion]
6:16mins
120
Work - I [Chapter 8]
5:17mins
121
Work - II
6:09mins
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