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# CES Mechanics II Lecture 1

RWTH Aachen University, Bachelor program in Computational Engineering Science

Topics:

• statics review
• outline of dynamics
• particle kinematics 1.1
• differentiation of vector functions:
• \frac{d \left( m \mathbf{A} \right)}{d u} = \frac{d m}{d u} \mathbf{A} + m \frac{d \mathbf{A}}{d u}
• \frac{d \left( \mathbf{A} + \mathbf{B} \right)}{d u} = \frac{d \mathbf{A}}{d u} + \frac{d \mathbf{B}}{d u}
• \frac{d \left( \mathbf{A} \cdot \mathbf{B} \right)}{d u} = \frac{d \mathbf{A}}{d u} \cdot \mathbf{B} + \mathbf{A} \cdot \frac{d \mathbf{B}}{d u}
• \frac{d \left( \mathbf{A} \times \mathbf{B} \right)}{d u} = \frac{d \mathbf{A}}{d u} \times \mathbf{B} + \mathbf{A} \times \frac{d \mathbf{B}}{d u}

Corresponding Gross et al. Kinetik chapters are shown in blue.

Key techniques:

• differentiation of vector functions

ConcepTests (RWTH only):

Why not try an online test concerning rectilinear kinematics? Online scoring may not work sometimes, but you can write down your answers, and compare to 1:d, 2:c, 3:d, 4:c, 5:a, 6:c, 7:c.

Review of statics:

• equilibrium if \mathbf{R} = \mathbf{0}, \mathbf{C}^R = \mathbf{0} (3D, 2D)
• what if not? dynamics!
• how to compute \mathbf{R}, \mathbf{C}^R?
• forces can be added to form \mathbf{R} only for concurrent systems
• moving action line of a force generates a couple of transfer \mathbf{C}^T = \mathbf{r} \times \mathbf{F}
• couples of transfer can be added to any other couples to form \mathbf{C}^R
• \mathbf{C}^R can be often eliminated by moving \mathbf{R} to a point where \mathbf{C}^R = \mathbf{r} \times \mathbf{R} (by -\mathbf{r})
• equivalent statements of equilibrium
• \sum F_x = \sum F_y = \sum M_O = 0 (general coplanar)
• \sum F_x = \sum F_y = 0 (concurrent coplanar)
• concepts: forces, moments, couples, distributed loads, friction, tipping
• techniques: FBDs, internal reactions, method of joints, method of sections

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