```python
import sympy as sm
import sympy.physics.mechanics as me
me.init_vprinting()
```


```python
m1, m2, m3, m4 = sm.symbols('m1, m2, m3, m4')
```


```python
N = me.ReferenceFrame('N')
```


```python
r1 = 3*N.x + 4*N.y
r2 = 3*N.y + 4*N.z
r3 = 4*N.x + 3*N.z
r4 = 4*N.y + 3*N.z
```


```python
first_moment = m1*r1 + m2*r2 + m3*r3 + m4*r4
```


```python
zeroth_moment = m1 + m2 + m3 + m4
```


```python
mass_center = first_moment/zeroth_moment
mass_center
```


```python
Ix = (
m1*me.cross(r1, me.cross(N.x, r1)) +
m2*me.cross(r2, me.cross(N.x, r2)) +
m3*me.cross(r3, me.cross(N.x, r3)) +
m4*me.cross(r4, me.cross(N.x, r4))
)
Ix
```


```python
na = (N.x + N.y + N.z).normalize()
```


```python
Ia = (
m1*me.cross(r1, me.cross(na, r1)) +
m2*me.cross(r2, me.cross(na, r2)) +
m3*me.cross(r3, me.cross(na, r3)) +
m4*me.cross(r4, me.cross(na, r4))
)
Ia
```


```python
sm.simplify(Ia.dot(na))
```


```python
Ia.dot(N.x)
```


```python
r_r = -3*N.y + 4*N.x
r_l =  3*N.y + 4*N.x

m = sm.symbols('m')

Ix = (
    m*me.cross(r_r, me.cross(N.x, r_r)) +
    m*me.cross(r_l, me.cross(N.x, r_l))
)
Ix
```


```python
m*me.cross(r_r, me.cross(N.x, r_r))
```


```python
m*me.cross(r_l, me.cross(N.x, r_l))

```


```python
Ix.dot(N.y)
```


```python

```

f6353afe9ee42b73198c577d045acde7568dce07
ipynb
Jupyter Notebook
content/notebooks/mass.ipynb
moorepants/me41055
5c941d28f6f61fa1a02fbda4772d88010014eec0
CC-BY-4.0
content/notebooks/mass.ipynb
moorepants/me41055
5c941d28f6f61fa1a02fbda4772d88010014eec0
CC-BY-4.0
2022-01-07T18:05:36.000Z
2022-03-22T15:15:01.000Z
content/notebooks/mass.ipynb
moorepants/me41055
5c941d28f6f61fa1a02fbda4772d88010014eec0
CC-BY-4.0
2022-01-24T17:18:40.000Z
2022-01-24T17:18:40.000Z
Qwen/Qwen-72B
1. YES
2. YES