Rotate log everyday on existing script

Shell Programming and Scripting
1

quick question:

I have a current script that will put the output on a log file. See snapshot of the code below. I wanted this to be rotated everyday based on date. So if anyone execute the script today there will be a filecreated such as sys.log.(datetoday), if tomorrow it would be sys.log.(datetomorrow)a

LOGFILE=/export/home/sys.log
echo "$DATE_STR - Script executed by $W " >> $LOGFILE

thanks,

2 
mv ${LOGFILE} ${LOGFILE}.$(date +%Y-%m-%d)

see man page for date for other format options.