Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Related questions
Concept explainers
Question
thumb_up100%
![Write the function with the following name twobody_dynamics_first_order_EoMs(t, states) that
describes the equations of motion you have derived above in Question 1.1. states represents the 6-dimensional
column vector X in Equation (1.1).
L]: # Run this cell, should import everything you need
import numpy as np
from scipy.integrate import solve_ivp
from math import pi, sin, cos, sqrt, acos, asin, tan, atan
import matplotlib.pyplot as plotter
21: # YOUR CODE HERE
raise Not ImplementedError()
Not ImplementedError
Cell In [2], line 2
1 # YOUR CODE HERE
2 raise NotImplementedError()
Not ImplementedError:
Traceback (most recent call last)](https://content.bartleby.com/qna-images/question/7830619d-3fbe-414c-9d12-28af960fe618/accaf603-22de-43e1-b5e0-ac4e5230ba88/8pi7eqj_processed.jpeg)
Transcribed Image Text:Write the function with the following name twobody_dynamics_first_order_EoMs(t, states) that
describes the equations of motion you have derived above in Question 1.1. states represents the 6-dimensional
column vector X in Equation (1.1).
L]: # Run this cell, should import everything you need
import numpy as np
from scipy.integrate import solve_ivp
from math import pi, sin, cos, sqrt, acos, asin, tan, atan
import matplotlib.pyplot as plotter
21: # YOUR CODE HERE
raise Not ImplementedError()
Not ImplementedError
Cell In [2], line 2
1 # YOUR CODE HERE
2 raise NotImplementedError()
Not ImplementedError:
Traceback (most recent call last)
Transcribed Image Text:1. solve a system of ordinary differential equations of first order numerically using solve_ivp.
2. generate plots after "solving" the differential equations using matplotlib.pyplot. In that tutorial, the
equations of motion described the dynamics of a simple pendulum. In this problem, you will investigate the
motion of a satellite orbiting the Earth. This is modelled as a two-body dynamics system. A brief outline of
what you need to do in this problem set is below and that is followed by a systematic set of questions towards
achieving specific objectives. You will find the tutorial a handty reference here.
In this problem, you will have to first create a Python function called twobody_dynamics_first_order_EOMS.
Given a time t and a state vector X, this function will return the derivatives of the state vector. Mathematically,
this means you are computing X using some dynamics equation X = f(t, X).
Once you have this function in Python, you can solve the differential equations it contains by using solve_ivp.
The command will be similar to, but not necessarily exactly, what is shown below:
solve_ivp (simple_pendulum_first_order_EoMS, t_span, initial_conditions,
args=constants, rtol = 1e-8, atol = 1e-8)
which integrates the differential equations of motion to give us solutions to the states (i.e., position and velocity of
a satellite). In the above, t_span contains the initial time to and final time tƒ and it will compute the solution at
every instant of time (you will define this later in Problem 1.3 below).
The integration is done with initial state vector Xo which defines the initial position and velocity. Xo needs to be a
column vector.
You will need to use the following constants in arriving at your answers:
• Earth gravitational parameter = 3.986 × 105 km³/s²
• Earth mean radius = 6378.14 km
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 3 steps with 1 images
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
![Plot the orbit in 3D using a suitably dimensioned sphere for the Earth.
[6]: # YOUR CODE HERE
raise NotImplementedError()
Not Implemented Error
Cell In [6], line 2
1 # YOUR CODE HERE
----> 2 raise NotImplementedError()
Not ImplementedError:
Problem 1.6
Plot the Specific Energies (i.e., all three Kinetic, Potential and Total Energy) in the same plot as a function of time.
The x-axis must show time (in hours) and y axis must show the Energy (in km² /s²).
[7] # YOUR CODE HERE
Traceback (most recent call last)
raise NotImplementedError()](https://content.bartleby.com/qna-images/question/7830619d-3fbe-414c-9d12-28af960fe618/5e15e086-efb6-4211-bedc-0aad6f43debe/naevtsp_processed.jpeg)
Transcribed Image Text:Plot the orbit in 3D using a suitably dimensioned sphere for the Earth.
[6]: # YOUR CODE HERE
raise NotImplementedError()
Not Implemented Error
Cell In [6], line 2
1 # YOUR CODE HERE
----> 2 raise NotImplementedError()
Not ImplementedError:
Problem 1.6
Plot the Specific Energies (i.e., all three Kinetic, Potential and Total Energy) in the same plot as a function of time.
The x-axis must show time (in hours) and y axis must show the Energy (in km² /s²).
[7] # YOUR CODE HERE
Traceback (most recent call last)
raise NotImplementedError()
Solution
by Bartleby Expert
Follow-up Question
Please guide
![Problem 1.3
Plot the magnitude of the position vector versus time. The x-axis must show time (in hours) and y axis must show
the radius (in km).
[4]: # YOUR CODE HERE
raise NotImplementedError()
Not ImplementedError
Cell In [4], line 2
1 # YOUR CODE HERE
----> 2 raise NotImplementedError()
Not ImplementedError:
Problem 1.4
Plot the magnitude of the velocity vector versus time. The x-axis must show time (in hours) and y axis must show
the radius (in km/s).
[5]: # YOUR CODE HERE
raise NotImplementedError()
Not ImplementedError
Cell In [5], line 2
Traceback (most recent call last)
1 # YOUR CODE HERE
----> 2 raise NotImplementedError()
Traceback (most recent call last)](https://content.bartleby.com/qna-images/question/7830619d-3fbe-414c-9d12-28af960fe618/ca1a8aea-3763-4f32-8744-4c5d3a4c74f4/0qreaj_processed.jpeg)
Transcribed Image Text:Problem 1.3
Plot the magnitude of the position vector versus time. The x-axis must show time (in hours) and y axis must show
the radius (in km).
[4]: # YOUR CODE HERE
raise NotImplementedError()
Not ImplementedError
Cell In [4], line 2
1 # YOUR CODE HERE
----> 2 raise NotImplementedError()
Not ImplementedError:
Problem 1.4
Plot the magnitude of the velocity vector versus time. The x-axis must show time (in hours) and y axis must show
the radius (in km/s).
[5]: # YOUR CODE HERE
raise NotImplementedError()
Not ImplementedError
Cell In [5], line 2
Traceback (most recent call last)
1 # YOUR CODE HERE
----> 2 raise NotImplementedError()
Traceback (most recent call last)
Solution
by Bartleby Expert
Follow-up Question
![Problem 1.2
Use solve_ivp to integrate the equations of motion of the two-body problem. The initial position and velocity
state vector Xo = (r, v)™ is:
and
3]: # YOUR CODE HERE
r =
raise NotImplementedError()
V =
The duration of the simulation is for one day but you should compute the solutuion for every ten seconds. We
show you how to control this below but you will have to make changes to this code to get it to work correctly for
this simiualtion.
Not ImplementedError
Cell In [3], line 2
Lastly, when using solve_ivp make sure that you use rtol=1e-12 and atol
[6510.759869015321
2676.16546382759 km
333.334029373109
[-2.232024608624287
9.49860960555864 km/s
1.18311436869621
1 # YOUR CODE HERE
----> 2 raise NotImplementedError()
= 1e-12.
Traceback (most recent call last)](https://content.bartleby.com/qna-images/question/7830619d-3fbe-414c-9d12-28af960fe618/17d05dcf-faaf-4dc1-b767-cbe87ed94449/suadwnm_processed.jpeg)
Transcribed Image Text:Problem 1.2
Use solve_ivp to integrate the equations of motion of the two-body problem. The initial position and velocity
state vector Xo = (r, v)™ is:
and
3]: # YOUR CODE HERE
r =
raise NotImplementedError()
V =
The duration of the simulation is for one day but you should compute the solutuion for every ten seconds. We
show you how to control this below but you will have to make changes to this code to get it to work correctly for
this simiualtion.
Not ImplementedError
Cell In [3], line 2
Lastly, when using solve_ivp make sure that you use rtol=1e-12 and atol
[6510.759869015321
2676.16546382759 km
333.334029373109
[-2.232024608624287
9.49860960555864 km/s
1.18311436869621
1 # YOUR CODE HERE
----> 2 raise NotImplementedError()
= 1e-12.
Traceback (most recent call last)
Solution
by Bartleby Expert
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
Transcribed Image Text:Plot the orbit in 3D using a suitably dimensioned sphere for the Earth.
[6]: # YOUR CODE HERE
raise NotImplementedError()
Not Implemented Error
Cell In [6], line 2
1 # YOUR CODE HERE
----> 2 raise NotImplementedError()
Not ImplementedError:
Problem 1.6
Plot the Specific Energies (i.e., all three Kinetic, Potential and Total Energy) in the same plot as a function of time.
The x-axis must show time (in hours) and y axis must show the Energy (in km² /s²).
[7] # YOUR CODE HERE
Traceback (most recent call last)
raise NotImplementedError()
Solution
by Bartleby Expert
Follow-up Question
Please guide
Transcribed Image Text:Problem 1.3
Plot the magnitude of the position vector versus time. The x-axis must show time (in hours) and y axis must show
the radius (in km).
[4]: # YOUR CODE HERE
raise NotImplementedError()
Not ImplementedError
Cell In [4], line 2
1 # YOUR CODE HERE
----> 2 raise NotImplementedError()
Not ImplementedError:
Problem 1.4
Plot the magnitude of the velocity vector versus time. The x-axis must show time (in hours) and y axis must show
the radius (in km/s).
[5]: # YOUR CODE HERE
raise NotImplementedError()
Not ImplementedError
Cell In [5], line 2
Traceback (most recent call last)
1 # YOUR CODE HERE
----> 2 raise NotImplementedError()
Traceback (most recent call last)
Solution
by Bartleby Expert
Follow-up Question
Transcribed Image Text:Problem 1.2
Use solve_ivp to integrate the equations of motion of the two-body problem. The initial position and velocity
state vector Xo = (r, v)™ is:
and
3]: # YOUR CODE HERE
r =
raise NotImplementedError()
V =
The duration of the simulation is for one day but you should compute the solutuion for every ten seconds. We
show you how to control this below but you will have to make changes to this code to get it to work correctly for
this simiualtion.
Not ImplementedError
Cell In [3], line 2
Lastly, when using solve_ivp make sure that you use rtol=1e-12 and atol
[6510.759869015321
2676.16546382759 km
333.334029373109
[-2.232024608624287
9.49860960555864 km/s
1.18311436869621
1 # YOUR CODE HERE
----> 2 raise NotImplementedError()
= 1e-12.
Traceback (most recent call last)
Solution
by Bartleby Expert
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- Write a JAVA program to add two matrix using pointers. JAVA program to input two matrix from user and find sum of both matrices using dynamic array.Example InputInput matrix1: 123456789Input matrix2: 987654321 OutputSum of both matrices:10 10 1010 10 1010 10 10arrow_forwardWrite a C Program to read a matrix and find sum, product of all elements of two dimensional (matrix) arrayarrow_forwardCreate a python program that will except a 3x3 matrix and unit for translation, then conduct a basic 2D transformation of translation on the matrix.arrow_forward
- Write MATLAB code. For input vector x, write a function to return vector y in which all the elements in vector x are duplicated. Example: If input x = [1 0 4], then y = [1 1 0 0 4 4].arrow_forward5. Find a closed form representation for the function defined recursively by f(0) = 5 and f(n+1)=2f(n)+4". Prove that your representation is correct using an inductive argument.arrow_forwardWrite program_ How to perform matrix operations in java?.arrow_forward
- Write a function in matlab that takes a matrix with m rows and n columns and returns the sum of all of the odd numbers inside of that matrix.arrow_forwardI need help with a MATLAB problem. The following code uses an ode45 function to integrate the Kinematic Differential Equations. What I want to do is C_ode * transpose(C_ode)? I can't do that because C_ode is composed of multiple 3x3 matrices. The function transpose dosen't support N-D arrays. So, how do I accomplish C_ode * transpose(C_ode)? I tried using CCT = sum(C_ode .* permute(C_ode, [2, 1, 3]), 1); but it gives me 3x1 matrices which is incorrect. C_ode * transpose(C_ode) should give the a 3x3 identity matrix. % Initial Conditionsw = [2;-1;1];T = 30;I = [150; 400; 400];EP = [0;0;0;1];C = eye(3,3);tspan = [0 20]; % Using ode45 to integrate w dotoptions = odeset('RelTol',1e-10,'AbsTol',1e-10);result = ode45(@K_DDE, tspan, [w; C(:)], options); % Extracting information from ode solvert = result.x;w_ode = result.y(1:3,:);C_ode = reshape(result.y(4:end,:), [3,3,length(t)]);CCT = C_ode*transpose(C_ode) function dwCdt = K_DDE(t, w_C) w = w_C(1:3); % corrected indexing for w C =…arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Database System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill Education
Starting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSON
Digital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSON 
C How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSON
Database Systems: Design, Implementation, & Manag...Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage Learning
Programmable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
Database System Concepts
Computer Science
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:9780134444321
Author:Tony Gaddis
Publisher:PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:9780132737968
Author:Thomas L. Floyd
Publisher:PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:9780133976892
Author:Paul J. Deitel, Harvey Deitel
Publisher:PEARSON
Database Systems: Design, Implementation, & Manag...
Computer Science
ISBN:9781337627900
Author:Carlos Coronel, Steven Morris
Publisher:Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education