I'm studying for my Final and having a hard time understanding the criteria for category (Sink, Spiral Sink, Center, etc.) and how to tell whether the direction is clockwise (CW) or counter-clockwise (CCW).
If someone could please tell me whether my understanding (typed below) is correct, I would really appreciate it!
Case 1: If $\lambda_1,\lambda_2>0$ and real, then it is a Source.
Case 2: If $\lambda_1,\lambda_2>0$ and complex, then it is a Spiral Source.
Subcase 1: If $\lambda_{re}>0$, then motion is CW.
Subcase 2: If $\lambda_{re}<0$, then motion is CCW.
Case 3: If $\lambda_1,\lambda_2<0$ and real, then it is a Sink.
Case 4: If $\lambda_1,\lambda_2<0$ and complex, then it is a Spiral Sink.
Subcase 1: If $\lambda_{re}>0$, then motion is CW.
Subcase 2: If $\lambda_{re}<0$, then motion is CCW.
Case 5: If $\lambda_1=\lambda_2=0$, then it is a Center.
Case 6: If $\lambda_1>0>\lambda_2$, then it is a Saddle.
Thank you in advance to anyone who can help!