Theoretical Mechanics

1.

Theoretical Mechanics
Rotational motion
Plane motion: positions

2.

Questions from the class
No questions this time
Oleg Bulichev
Theoretical mechanics
3

3.

Quiz 1
Oleg Bulichev
Theoretical mechanics
4

4.

Motion representation
More info 1
More info 2
Oleg Bulichev
Theoretical mechanics
6

5.

Linear and angular parts for rigid body
Core idea is to think in terms of bases and vectors
Oleg Bulichev
Theoretical mechanics
7

6.

Task 1 (yours)
Oleg Bulichev
Theoretical mechanics
8

7.

Task 1 (yours): right figure
Oleg Bulichev
Theoretical mechanics
9

8.

Task 2 (mine)
Oleg Bulichev
Theoretical mechanics
10

9.

Task 3 (mine)
Oleg Bulichev
Theoretical mechanics
11

10.

How to find velocities and acc of a rigid body
Oleg Bulichev
Theoretical mechanics
12

11.

Task 4 (mine): Simulation
Oleg Bulichev
Theoretical mechanics
13

12.

Task 4 (mine): solution
Oleg Bulichev
Theoretical mechanics
14

13.

3 typical approaches for kinematics
Triangular
Geometrical
Vector-based
Consider a mechanics
as a set of triangles.
Represent a mechanism as a set
of figures (mainly circles and lines)
Represent a mechanism
as a set of vectors
Solution based on
Sin and Cosine rules
mainly.
Solution based on
Solution based on
Finding intersection b/w figures
(line-line,circle-line,circlecircle,sphere-line). Need nonlinear
solver!
Writing a system of
nonlinear equations and
put it in nonlinear solver!
+: fast, easy to code.
-: applicable only for
simple mechanisms
+: Solve most of mech.,
choosing roots are intuitive
-: difficult to imagine
Oleg Bulichev
Theoretical mechanics
+: Best for tough mech.,
easy to imagine
-: Need to prepare a
solver for finding roots
15

14.

Task 4 (mine): Simulation
Oleg Bulichev
Theoretical mechanics
16

15.

Week HW
Grading
1.
2.
3.
HW costs 4 point max (All week HW costs 20 points). There are 6 HWs -> one extra (safety bag).
Not late policy. If you submit it later, 0 points.
Grading correct algorithm and idea - 2 out of 4 for sure.
Tasks
1.
2.
3.
4.
If task has label “coding”, it should be not only solved, but also coded.
It’s a good practice to code not coding task, for checking your calculations (not obligatory).
Consider, that this report you are making for yourself to use it in future. I mean, it can be helpful sometimes to
put full solution, not like “(1) eqn -> after trivial magical passes (2)”. It’s recommended to explain each step (it
helps you and me to find mistakes and typos)
Each HW is a report. It consists of a solution (don’t forget about formal criteria), info about tools which were
used, link to the code.
Formal reporting
1.
2.
3.
In Moodle you are sending only a report (other stuff are links).
Solution can be a photo of a paper sheet + plots, simulations from the computer.
We are in IT university, hence it’s obligatory that your code should work on other computers.
Oleg Bulichev
Theoretical mechanics
17

16.

Week HW1, Task 1 (Coding)
Oleg Bulichev
Theoretical mechanics
18

17.

Week HW1, Task 2 (Coding)
Oleg Bulichev
Theoretical mechanics
19

18.

Week HW1, Task 3
Oleg Bulichev
Theoretical mechanics
20

19.

Deserve “A” grade!
– Oleg Bulichev
[email protected]
@Lupasic
Room 105 (Underground robotics lab)